I believe what you are looking for is 'checkpointing', and the way to do that would be via an HDF5 file. Write it periodically, and then read the latest solution from the file if your time is up.
Incidentally, I thought the AdaptiveLinearSolver didn't run in parallel. 1 core for 24 hours + is quite the load. You might get a faster solution by just refining the crap out of your mesh and doing a regular linear solve no? Unless the adaptation is what you are after of course.