This "frozen and thawed" backup issue caused me many headaches over the years. Both ArcServe and Symantec Backup Exec were the culprits, on different machines. It effectively broke the backup chain (Full, Differential, Log), which I discovered when I attempted to restore to point-in-time, and was only able to recover to Sunday night.
Finally I got the attention of our system engineers, who were able to exempt my data drives from their backup, and they now backup only my SQL Backup drive, and not my SQL Data and SQL Log drives.
Senior Database Administrator
1st Source Bank