Should the route be changed if the GPS RAIM prediction fails?
The answer to this question will probably depend on the equipment involved and type of route being flown; as asked, the question is open ended, and there are several types of operations where the answer is a definite "no" (i.e. you do not need to adjust your route), while in other situations, that answer might change.

If you are flying on Victor airways using VOR receivers, then the answer is certainly "no".  You aren't navigating with GPS, so you don't care about the RAIM.

If you are flying in RNP-3 or RNP-10 airspace (i.e. the required navigation performance is 3 NM or 10 NM -- so your INS can drift that far before you need to do something different) with an INS or multiple INS's, then you probably don't care about the RAIM... your INS's won't drift that far in several hours, and the RAIM should be back to acceptable limits well before then. (Maybe there are exceptions to this; I'm not aware of any.)

If you are flying an approach where GPS is your primary navigation, then YES, you absolutely do need to change your plans if the RAIM fails.  Break off that approach, go somewhere where the RAIM is good, use a conventional navaid for the approach, whatever the best option is for you.

I'm not aware of any enroute operations where RAIM is a factor; what I'm flying has dual INS's and the FMC can update its position off of not only the GPS but also from conventional (DME/DME, or VOR/DME) navaids, and we don't worry about the RAIM enroute, even when flying Q routes where GPS is required.  (Maybe that's a hole in our OpSpec, I dunno.)  We do look at it when flying an RNAV approach.