ScrObot

I believe a dropship has enough fuel to traverse the entire map. I've never been unable to reach a remote site even with the starting Charlie.

I have the exact same issue. My 1.07 save was in ground combat. Steam upgraded to 1.08 today, and when I completed the mission and went back to base (in a Shrike), I got the "No soldiers present at this base" message. They are all there in the Barracks tab. I also had one empty Charlie at my base, and a bunch of unassigned soldiers. Once I assigned a soldier to the empty Charlie (thanks derdax!), the Soldier Equipment screen worked properly again. (However, if I unassigned them, I get the "No soldiers" message again.) This is new in 1.08 (I did not update in the experimental branch), as I had that empty Charlie in 1.07 without issue. Note: was in my first base (of 3, with one more currently being built).