Will using the FixMBR option in Partition Recovery for Windows lose any of the data that I am trying to recover?

Here are some things you should do first. You can backup existing partitioning information first before you do that. Select the drive in question on the left side and then select File - Backup Partitioning Info. You can revert back to that if needed.

Also, in case you have performed a super scan, you should save the scan results to avoid having to scan again.

Select the Scan Results on the left side of the screen and select File - Save Scan Results. You can then reload those later. The FixMBR does not delete data, just replaces 1 sector at the very beginning of the drive.