If the remote is a RF remote and the DVR is located to close to the PS3 then the PS3 turning on could have two issues which could cause the remote to stop working.
1. The PS3 is using wi-fi to connect to your home Internet connection. This is causing RF interference with the remote, which is causing it to fail. Fix problem by hard wiring PS3 to your Internet connection, or trying relocating DVR or PS3.
2. The PS3 has a hard drive which spins up which gives off a small electromagnetic field which is falling right across the DVR. Fix problem by moving PS3 further away from DVR - typically a few inches will do the trick with this.
Off topic (kind of)...
Digital video recorder (DVR) vs. PVR - personal video recorder - the PVR is typically reserved for things like an iPod video which is 'personal' versus the DVR which is used on shared displays. The Archos products are PVRs, while Tivo, Cable, and Satellite digital recorders would almost always be called DVRs.