We have the same type holes as you are tlaking about.  We used to cut out a two foot section of the pipe, and replace it.  The second year there is a sink hole there again, dig it up again and find that the varmint has eating a hole in the new connector.  After that we just dig down to the hole, split a piece of tile length ways to make a patch and then put a half bag of quick crete over the patch.  This seems to work pretty good.

You guys talk about them digging down to the tile, I'd say they are getting in somewhere else and then eating the hole from the inside out.  We had a muskrat that went up a tile line about 600 feet before he got stuck.  Tile started 8" and when it got down to 4 he got stuck.  That was nasty to clean out.