Hi welcome to our forum. You don’t need to connect a Foxsat-HDR to a router. This could be down to overheating, worth disconnecting the box and taking the lid off and vacuuming out any dust. Check the hard disk fan spins easily and isn’t seized.
At that age you may need a new hard drive, check this by disconnecting the hard drive power and data connections and check if the box now works without losing the video, The time shift buffer file may be corrupted, anyone capable of connecting the drive to a Linux booted PC can normally fix this by renaming the file 0.ts to say 0.old to force the box to create a new file.