How can I fix my TV model No L17LID648 remote control?

Logik 19" TV
Model : L17LID648
Serial Number : 913010682
The TV works fine at first, recieving all the chanels that it should but after it has been on for a while(No particular length of time) the remote control ceases to work at all, neither changing chanels or changing settings or even switching on or off.
I have tried several new sets of batteries in the remote but they have no effect.
The controls on the back of the set still work OK.
When the set has been switched off for some time and switched on again it starts working properly again for a while but then the fault recurs.
Would replacing the remote be likely to cure the problem or is it more likely to be something inside the set itself?
Before finding this website I ordered a new remote control which I have not yet recieved.