Im guessing rules vary according to nation and company requirements.
At my outfit during the EDTO period if an airfield becomes unusable we have to recalculate for a new airfield. Once airborne we only have to consider whether an approach is likely to be able to be carried out, there aren't set limits like there are when planning. This makes the likelihood of an airfield becoming unusable pretty unlikely.
Practically speaking if the EDTO range circle you are currently in becomes unusable you would most likely continue on. If however an EDTO alternate further on becomes unusable, and another alternate cant be made to work in its place, you would probably need to divert prior to exiting the current circle.
Operating outside of EDTO circles without an emergency requirement could have all sorts of repercussions.