My current setup probable has 12 feet of hose between the reservoir tap and the furthest of four autopots, and something like two feet of head, and it works perfectly. The autopot kits (my two orders at least) included fittings that allow use of standard 1/2" garden hose as the main feed line, and necks down to the ~1/4 black line that attaches to the auto valves. If you use half inch hose to reach the vicinity of the autovalves before necking down, you could place the reservoir a lot further away than I did.
The valves will work fine with not much head, likely a foot or so would be fine. If you go with higher head, the max fill in the pot may increase slightly, but not by much. In any case, something like a couple feet should be perfect. If you want to do a long run from the reservoir, just do most of it with 1/2 hose and you will be golden.