I would suspect that your lift pump is weak. Going up a hill forwards lowers the level of the fuel in the tank relative to the pump and makes pumping harder. Going in reverse, raises the fuel level with respect to the pump and you almost have a gravity feed situation.
Here is my list of things to check when apparent fuel flow problems rear their head causing shutdown, stuttering or power loss.
1) Check the air filter and fresh air plumbing to the filter housing.
2) If just power loss, check for exhaust restrictions in the muffler and the exhaust manifold
3) Disconnect fuel line to the IP and check for fuel flow, should be substantial when the lift pump is active.
4) Disconnect fuel line to the lift pump, should be a good flow
5) Disconnect fuel line from tank to the first filter, again should be good fuel flow
6) If 5) fails, there is an obstruction in the tank, either clean out the tank, or for temporary relief, blow back air into the tank
7) If 4) fails, either 6) or the primary filter is plugged, replace
8) If 3) fails, either 6), 7) or secondary filter is plugged, replace
9) Check all the fuel lines for cracks or pinholes, may show diesel contamination, maybe not, but will allow air infiltration into the fuel system.
Filters plugging up are the consequence of dirt or junk in your tank, or in many cases algae. Clean out your tank, and/or use an algae inhibitor in your fuel.
If possible, buy or fabricate a screen for the fuel inlet to your tank , something like the one shown.
Try to keep your tank full after each use to minimize condensation and water problems in your fuel tank. Water in the tank causes running problems if it is the in fuel stream to the engine, as well as causing rust problems on the fuel sending unit, and algae build up which will coat and clog your filters with black particles or slime.