Thomson (TG or Speedtouch) ADSL routers which you may have bought yourself or received from your ISP, (for example O2/Be Boxes are TG), are very prone to over-heating. This can cause strange symptoms of which the need for a reboot of it is the most common.
The centre of the top will be very hot.
The first thing to try is to prop one side up by about 2.5cm/1”. This creates a through-flow of cooler air and very often solves the problem. Shading from direct sunlight will clearly help as well.
It is possible similar solutions could apply to other ADSL routers.
If this doesn’t work then it looks like you have an actual fault beyond the technical scope of this site sorry.