Hi,
There is no option to pause and resume the execution at any time. However, there is something close to what you are asking for.
The execution makes several passes through your code. If you use the option -keep-all-files (at the cost of storing many files), at the end of each pass, all information from that pass are stored. You can then stop the execution after a certain pass and later resume from the last completed pass. See more details in this answer about Recovering data after abnormal termination.
However, in your situation, a better workflow might be to use a dedicated server for the analysis and free up your desktop. You (and several other developers) can submit analysis jobs to the server. The jobs are queued on the server, and as the server becomes available, it runs the next available job. After the analysis is complete, the results are downloaded back to your desktop for review. See Polyspace Analysis on Clusters.