First thing. Is it turning itself OFF? Do you have to control it manually when that happens?

I can only think of a couple of things that might cause that to happen.
Have you set the Autopilot to catch the ILS and Glide Slope (pressed the LOC button followed by the APP button on the MCP)? I find I must press the APP button when below the G/S.
Have you set an ILS runway, STAR and TRANS in the FMC?
You can also check for an END OF ROUTE message on the FMC. The Autopilot switches to ALT HOLD, SPEED HOLD and HEADING HOLD if that message appears (I think). It's a long time since I have done a flight without using the FMC program with ILS, STAR & TRANS.

Assuming that you have done all that, I can't think of any other reason for the Autopilot to cease to function.

Mark