ThinApp does support multiple reboots during a capture. When the first reboot has finished and you see Setup Capture simply kill it by pressing the close button in the right top corner (red one). Do not press any other button within the Setup Capture window. This will stop Setup Capture from deleting the snapshot file.
When you have done the last reboot run Setup Capture again and it should find the current snapshot file and ask you if you would like to continue.
If by some chance your reboot fails to show the ThinApp continuance upon login after a reboot, it's possible your application erased the contents of the HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Run key.
Just after completing the ThinApp Pre-Installation Setup Capture but before installing the app, go into the registry and save this key. There should be an entry called “Thinstall Setup Capture Continue” which will have a bunch of command line switches to the SETUP CAPTURE.EXE in it. This is what is used to tell ThinApp to pick back up where it left off.
You should be able to save this and restore this after completing the app install.