Okay, so your experience seems similar to mine... I apologise now for a very, very lengthy post - but I'm hoping by explaining my journey that it helps you to maybe get a faster resolution.
The short version is: I had issues similar to yours, and have been through all kinds of frustration in getting them sorted. I recommend going with an ISP that can give you a phone line and fibre (stops cross-blame), and go for one that offers OpenReach's Enhanced Care option on the line. Also go for an ISP that has a good history of holding OpenReach to account. The Enhanced Care gives a 24 hour SLA and means that OpenReach have higher penalties for not meeting it. It gives a minimum connection speed, and it means engineer visits can occur 24x7 as long as you give access to them.
Long version:
I was with TalkTalk ADSL, it kept dropping out. Sometimes it went a few months, then would drop out badly for weeks or months, then settle down, then start again. This was a backup to my VM cable connection and TalkTalk were useless in trying to sort it. Quite often their broadband department would pass the ongoing ticket to the TV department. I couldn't get through to anyone competent except the retentions department...! They understood the issues as a number of them were ex tech team, but they couldn't get anyone in the current (at the time) tech team to resolve the problems. In the end I kicked them into touch when they were raising costs twice in a year and had to allow people to break contract.
I went about 6 months without a backup connection. After my VM cable connection started playing up, I realised I did need my backup line as I work a most the time from home and the office is several hours away. I went with Sky for ADSL. Connection was stable for some time, but then the same pattern started. Sky raised several calls to OpenReach across two distinct separate sets of incidents... They kept not getting back to me when promised, I was doing all the chasing and we were getting nowhere.
FTTC became available at my local cabinet, and I was going to ask Sky to release me from my contract given their catastrophic failure to even attempt to resolve my problems. They offered me a deal to switch to fibre with them and a promise they would sort out any issues if they remained after switching to fibre. I guessed switching from ADSL to fibre with them would be the easiest move, and with the promise I could ask to leave if they didn't get them sorted.
Moved to fibre. Everything was fine for a week or two, then dropouts started occurring constantly. It might be fine for a few hours, but I couldn't get past a few hours of the connection being up. After an initial call to the normal tech support line to be told nothing was wrong (!) I contacted the Chief Execs office and the issue was passed to the Exec Tech Team.
I had four visits to the exchange and to deal with issues outside the property, things weren't resolved.
I then had 6 engineer visits to my home. During the first they found an issue in the cabinet, signed off the line as being perfect - no HR, no noise, attainable rate of 120mb/s.
The second engineer visit saw the line again confirmed as absolutely perfect "I'd love a line to the cabinet of this quality" being the phrase used. At the end of this visit, and a bit perplexed by what the problem could be, the engineer suggested swapping the router (cables, filters, different power sockets had been tried before this and I was waiting on a new router from Sky later that day due to their restrictive T&Cs).... He said that if the router swap didn't solve the problem then it could be the port on the DSLAM or the power card in the cabinet and a lift and shift would be the next thing to try.
I then had 2 more engineer visits where the engineers all wanted to do lift and shifts, but the DCO wouldn't let them. All engineers were perplexed and all went through motions to make it look as if they'd done something on each visit - they re-terminated the overhead line on both sides (one side per visit), switched to the spare pair from the overhead cable... Ultimately just making changes to something that was showing as perfect on all their kit. REIN was checked inside the house and signed off as not being an issue.
I'd been told after the third visit to my house that it was down to me to prove that there was a problem on OpenReach's network and not in the house (I'd also been told to move home to solve the problem!) - I setup a Splunk server and forwarded the syslog events from the Sky router and RouterStatsLite to get connection drops, speeds, SNR margin, etc... Then I created nice, easy to understand graphs in Splunk that showed the dropouts of the connection and some wild SNR margin fluctuations at completely random times.
Initially Sky, OpenReach and the engineers didn't seem interested in the data I'd got and prepared at much effort. None of them seemed to be also checking the connection details they had which would have shown the same issues. I was getting drops sometimes 158 times a day!
As the engineer was coming to me for the fifth visit, he apparently had a call from someone quite high up within OpenReach as I was starting to affect their stats on repeat visits. He was told to do the lift and shift and replace the underground cable between the pole and the cab. He did both, didn't resolve the issue.
For the sixth and final visit, the engineer did a REIN check and also did something at the Exchange. He said he wanted to do a cease and re-provide but the DCO refused permission. After this visit I got the line to stay up for 3 whole days, I thought the problem was sorted but alas it wasn't.
By this point, and with Sky seeming to get caught up with OpenReach process but unable to get them to sort the issue I decided to go to Zen and add Critical Care. From a customer service perspective, despite a bit of a bumpy start, the Sky Exec Team had been excellent. Unfortunately the faceless part of OpenReach were going against their engineer's expert knowledge and on the ground assessment/decisions. I knew that issues like this may take a bit of time to resolve as things are worked through - but for the most part the line between myself and the cab just kept being rechecked and signed off.
Anyway, I ordered a brand new Zen line, and it's taken almost three weeks to get in (and almost 4 since the last engineer visit). Ironically the Sky line has been rock solid for the past 7 days. I can't fault it in any way. I'm glad it is sorted, albeit too late for me to use.
Something was causing the dropouts. Something was wrong with the connection and I think somewhere between the cab and the exchange given that it affected both the ADSL and fibre connections. I wonder if OpenReach figured it out but knew it would take some time to resolve which is why they kept refusing to let engineer do things they felt was the next to carry out for troubleshooting.
As I said at the top of the post, all I can suggest is going for it, but go with a provider that offers Enhanced Care (Zen call it Critical Care, most others call it Enhanced Care). I wish I'd done this in the first place. Once you're up and running and everything's rock solid, you could consider dropping Enhanced Care after the initial contract period if you no longer need it...