Answers

1) Fiberglass tubs are notorious for getting hairline cracks that usually open up when someone is standing in it with the water running.

2) Also it might be a leak from upstream (plumbing behind the walls going in) such as a leaking copper pipe or loose pex fitting. It could also be in your drainage as well. 

3) Is it a one piece shell? Sometimes fiberglass units come in 1, 2 or more pieces and can leak at the seams. Use a sealant to fil in these seams if you have any. 

4) I've actually seen windows in a tub unit leak rain, etc behind the unit and it appeared as if the tub was leaking. 

Your best bet may be to pull out the unit and see where the leaking appears to be happening. 

Good luck!