Starting the car when facing up hill!

Hi. I have had two (same) problems when I have parked facing up hill. Basically, the car will start normally BUT after two seconds, it cuts out. The AA were called and he "pumped" the fuel through using the bellows (over the engine). After that, the engine started perfectly.
He asked when I had replaced the fuel pump and I told him never. He said that could be the cause.
Got the filter replaced and the guy in the garage said that the problem shouldn't happen again.
It did just last week (on holiday in Scotland). Again I was parked SLIGHTLY up hill and the car fired and then cut out after two seconds. I did the pump of the bellows and she fired.
If I park on the level or down hill, there is no problem.
This only seems to happen when I have half a tank or less. It's as if the fuel drains back into the tank. I would think there light be a slight air leak somewhere but just wondering if anyone else has had this problem.
We are looking at getting a new 208 in April, but don't know whether to ask the dealer about this problem (with the new 208) as we are part "X"ing the 207 and we want a good price!!!
Look forward to your reply and thanks in advance.
Castie.