Some further info. My wife was using her daughter's computer this afternoon, which is wired into the modem and her internet connection was working. Then my computer dropped out and stayed out for several minutes, her wired connection worked the whole time. So I quickly took the laptop out and booted it up. I was unable to get an internet connection over the wireless. I then moved the laptop into the same room as the modem, about 2 metres away from it. No connection, hers was still working.
So I think this confirms that the modem itself is flakey! Or at least the transmission part of it. I would expect that boosting the signal is not likely to help the situation either.
It looks like yet another call to Telstra! Last time we were on the phone for at least half an hour...and that is after we got through to the right person!