I think the best solution is to plan how long you can do with out the rod, then grab the offending cork, give it a good sharp twist to separate it - then send it in to get fixed.
I think it is only a matter of time until it happens while you are fishing. The constant flexing will eventually break what is clearly a poor bond. If you know you are going to have some down time from fishing it may be best to get it done then as at least you will have some control over the situation.