Stormy, when you use that reset button you're refreshing the ADSL connection, which is what we've been talking about.
You shouldn't have to do it too often.
ADSL performance is affected to an extent by line length (ie, distance from your exchange). I think the current max distance is about 3km, but Telstra is upgrading that to 5. Don't know if they're doing that retrospectively to already-ADSL-enabled exchanges, or if they're only doing it to exchanges being newly enabled for ADSL.
Anyway, if you're near the max permitted line length, then any little glitches in the line are more likely to cause an ADSL dropout. If you feel able, check all connections in the phone line that services your computer. Make sure the contacts on all connectors, plugs and jacks are clean. Open up junction boxes in the route between the telephone entry point to your house and your computer and make sure that any joins inside are electrically sound - ie, clean conductors twisted tightly together and clamped with a screw device of some kind - and insulated from each other. (You can buy those connectors at any electronics hobby shops - Dick Smith, Tandy, Jaycar, etc. Electrical contractors use large ones for house power - they would work too, but they're really too big and clumsy for a phone application. But they'd work at a pinch.)
If you have one of those large, cream coloured flat Telstra connectors with four fingers and the covers are not sealed (ie just held on with a screw), open those and check them too.
Reason for this suggestion - personal experience. In my last house, one telephone wall socket was subject to damp and the connections kept corroding, wreaking havoc with line quality. Also, I found an ants' nest in the outside Telstra junction box. Formic acid combined with the voltage on the phone wires had just about dissolved two of the wires!
CAVEAT: You're allowed to fiddle with any part of your household phone wiring downstream from the Telstra entry point. The junction box at the entry point should only be opened by a qualified technician - not necessarily Telstra, just a qualified person. (I qualified myself
)
Cheers
AA