The root cause is moisture on the membrane. Reservoirs are usually closed environments with liquid in them, so the air in them is going to be humid. It is only natural that at 100% relative humidity condensation may occur on the walls of the tank. It will be dripping on the membrane just the same. It's a natural phenomena, nothing we can do about it. Like when you're at the spa and water is dripping on the windows at the indoor pools. It's inevitable.
I say the membrane is not fit for the purpose and in extension this is a design fault (and I hold my stance on this claim). It can only work whilst it's dry. Once it's saturated, it blocks air passage.
I have the same track record with my Leakshield, with the membrane getting clogged, then the pump activation goes up and start to give off false alarms because of the repeated activation in short bursts.
You can find my posts on this forum about the same reports. I only replaced the membrane once till I figured this is going to be an uphill battle.
I'll be honest with you. I have no solution to it. The support dismissed the case. The forum members' mileage may vary. Some use it without trouble, and then there are those like us with the issues.
I suppose you could air-dry the device for a day every time this happens and make it into a maintenance habit...
Mine had just been demoted to an expensive tank cap... I can't be bothered to open up the case and take off the Leakshield every week.
If you have two Leakshields and are willing to experiment with one of them at the expense of its service life, then you could try using it without the membrane. This should remove any resistance in the air passage, so the pump could build up pressure effectively in the whole loop, instead of just pumping that tiny pocket behind the membrane in short bursts (and wait till the pressure equalises on the two sides of the membrane).
But be warned that the pump won't be sealed against the fluid then, so even if there's no direct contact, the moisture would get in the pump. I haven't a clue how resistant the internals are against moisture, so this could either be a long or a rather short experiment before the device malfunctions. You may also start to lose some fluid over time in the form of evaporation, as the pump would then just extract it without the membrane. Effectively you'd have an open loop this way - still pressurised of course, but with a clear path for evaporation to the open air.
Let us know how you get along, if you do this experiment.