Fact is that ADSL connections can drop at any moment from an electrically noisy milk float to a light switch causing ADSL to drop out if the noise spike is long enough and bad enough.
When you have the drop outs does the modem show the ADSL signal has dropped, if using WiFi check that it is also broken on Ethernet, since WiFi can be subject to its own set of problems.
When those 'BT engineers' say the service is shared with too many people, sounds like they are engineers who know very little about how ADSL works, since your ADSL signal is NEVER shared. Once your connection reaches the exchange and meets with other users it is shared, but this should not mean it stops working intermittently.
First step is to determine whether the ADSL signal is the issue, or it may be something network based.
NOTE: You do not have to remain with BT there are other providers you can join and you can also buy premium care levels if the odd drop-out is a major problem for you, but if its an ADSL service still they cannot guarantee you will not have any drop outs.