I've experienced that quite a bit, although for me, it's my neck/back muscles that really start feeling weak and incapable of supporting myself. It gets to the point where my muscles have actually felt painful and strained just from trying to sit up/stand.
I couldn't tell you what exactly is causing it however I do have crappy adrenal function, poor thyroid function can make you feel weak and floppy as well, I also have had inconsistent thyroid values on tests for some time, as well as a throughly established history of hypothyroidism on the maternal side of my family.
That sort of BP would have me feeling pretty lousy, I've gotten down to 108 systolic, and I felt like I couldn't stand up properly.
Try having some salt and getting your BP up a bit perhaps if you can do nothing else.