Wiring Leading to DSL Problems
I'm not sure this is within the scope of DIY but DSL issues are almost always a result of interference on the line.  A site like dslreports.com would probably be a good place to start.  Either way, I'll type out a long winded answer because I spent a few years doing DSL troubleshooting for earthlink a while ago and this is an issue near and dear to my heart.

Also, I would find out exactly what the ISP means by "Everything looks good".  They certainly have specific things they are measuring for so you will want to find out what those things are.  My guess is that they just came out while it was working and ran some line tests which usually won't exactly tell you much about when it's failing.  Also, do they see the connection drop from their end when the problem happens?  The phone support techs should be able to answer this (from authentication logs) if you don't already know.

If the connection is fine most of the time but occasionally stops working (as in the sync light on the modem/router goes off), then the techs that come out aren't going to find a problem because when they are there, it was working fine.

Possible sources of interference for DSL are numerous. 

Landline phones being unfiltered - All sides of every path the phone lines travel that do NOT lead to the modem need a filter.  This is frequently done either via a single filter in the box on the outside of the house if your modem has a dedicated line from that box with nothing else on it.  If that isn't the case, you need to have a filter on every other device that uses the phone lines.

Wireless landline phones (not cell) - the wireless frequencies by some phones will cause interference with the DSL signal.

Home security systems - these frequently phone home occasionally and are often missed when installing the above filters.

Speakers - if your phone line happens to run along the wall behind a pair of entertainment speakers, you might have problems there.

Microwaves - pretty unusual to have a phone line running near a microwave but it will likely cause problems if it does.

Basically, almost anything inside your house that uses electricity can cause interference for DSL lines which is why they always recommend you get a dedicated line ran from the box to your modem and that the line be as short as possible.  Try paying attention to what else in the house is being used when the internet cuts out (and verify the modem loses sync when it happens).  If the internet cuts out when someone turns on a light in a specific room, or when the TV is turned on, or the AC kicks on, (etc, etc, etc) then you will have a better idea of where to start looking.  If possible, at least temporarily, put the dsl modem as close (measured by length of wire needed to hook it up) to the box on the outside of the house as possible.  Then run networking cable inside the house (this is temporary..run it down the hallway if necessary) to the computer(s).  If you can unhook all the telephones long enough to troubleshoot, that would also help.  Just unhook all the lines out in the box besides the one going to the modem.  If the problem goes away, start plugging phones and other stuff back in until it comes back.  By process of elimination, you should be able to figure out what is causing the issue and maybe even be able to determine how to fix it.

As for who to call to fix it.  I always like to chat up the techs that come out to find out if they seem like they know what they are doing or if they are just following a manual.  If they know what they are doing, I will usually try to get their personal contact info (even just an email address) and work something out with them on the side if a need ever arises.  some will, some wont (they really shouldn't since they are likely not insured themselves and work won't be happy if they find out their techs have been moonlighting with their customers) but generally speaking, most of them can always use the extra cash on the side.  Failing that, I would simply ask around.  Everyone knows someone who has a wiz-kid who understands computer networking and you can probably get the problem fixed for far less than an electrician charging $100+/hr.