Unfortunately, campaign progress is stored locally. So if you install on a new computer, reinstall after a format, or the data somehow gets corrupted (with a crash for example), the progress is lost.
Aside from starting over, you can use the cheat codes to jump forward to where you left off. One caveat though is inventory items. Since there’s no record of which units were carrying what, the items won’t be what they were in the actual play though.
See here for the cheat codes that jump you to any mission you want: