I have a problem with wallet synchronization. After restart, synchronization does not resume. It is keeps saying, "Connecting to peers." I did a Veil wallet reinstallation and sync, but that doesn't fix the problem. There is no shift even after a few days.

If you are looking to send coins then try minimizing this window and send, it might work. I had same problem but transfers worked for me.
Also, if not already, ping this guy, he'll help you out with veil technical problems:
https://t.me/GrumpyVeil