I normally give an ADSL modem a lifetime of 4 to 5 years.
Normally when I see this kind of issue the basic troubleshooting I'll do is move to a different power outlet and change the power cable. But it usually comes down to a problem with the box itself.
Are you 100% sure the modem is powering itself off? Does it get hot when left on?
Intermittent connections can be caused by a line fault, exchange fault or internal CPE fault. Just keep an eye on it when its going off. Make sure the power light remains (green, not red, some modems don't have 2 colours) and watch that the DSL light isn't flashing or off. If after 2 weeks when the connection starts to get intermittent, the DSL is intermittent it means you've got an intermittent sync.
To be honest though this kind of problem, where the connection will be perfect for 2 weeks and then go bad, you're looking at a heat problem and your modem will need to be replaced.
In my experience, the tell tale symptom is the heat coming from the box so check that when it starts to go bad. It could mean solder melting and settling when cooled again.
My main suggestion to you: Find out whether its actually rebooting or if its losing sync (DSL light going off/flashing)
Edit: If you do plan on replacing the modem, ring your ISP first. They'll normally do it for free or quite cheap. Otherwise get a better brand modem.