Skidmark made a solid suggestion, assuming that you have/are willing to install the general DSL software on your pc. The key factor here is that you mentioned using a Linksys 54GS with random drops. Have you logged in on your router to check status and and try to reconnect?
I have used Linksys for the last ten years, but when Cisco entered the picture and customer service went to the Phillipines... Given that they have been out four times to no avail begins to point the finger at your router. I had to deal with replacing my 54GX three times and upgrading firmware twice due to poor design to resolve a similar problem. On the same note, after updating the firmware and checking everything multiple times for my in-laws on their Linksys router, the same problem (for them with cable!) never went away. Trying to help resolve their issue, for the heck of it I sent them a "pricey" Trendnet router
to replace their Linksys to see if that would help isolate the problem, and low and behold, for $10 their cable has yet to drop again... To boot, if I recall correctly theirs was also the 54GS (though could have been G or GL).
So, you may want to waste $10 and give that a try, and it's always good to have a backup router on hand should a lightning bolt fry yours at 11:58 pm as you're trying to file your taxes online the last day.
Also, as Skidmark said, your Speedstream will get hot, stay hot, and be just fine hot. It sounds odd that the problem continues - if a swap for your router doesn't help alleviate the issue, you may want to inquire if they have swapped you over at the DSLAM, granted if it were an issue there your service would simple completely disappear rather than go on/off at random.