I think you may be hitting the limitations of the battery technology. The more current you draw the harder the battery chemistry has to work to deliver that current. So it heats up, increasing the internal resistance of the battery, which means more volt drop internally, so less delivered to the system. The more time spent on high current draw the more the voltage sags, until the low voltage cut off kicks in and turns the system off. Meanwhile the battery chemistry is still working away converting chemical energy into voltage(potential). So when you turn back on it will power up because the voltage has come back up. But if you imeadiately start to draw top current again, voltage will quickly sag again to cut off.
From what you say it seems that you are doing the equivalent of jumping in the car, putting the peddle to the metal and leaving it there. That's fine if that's what you want to do, but it will give less range and shorten battery life.
I don't know what current rating your controller is, so don't know what you are pulling in pas5. But assuming 1000w, that's around 21A at 48v. That's a lotta juice. What is the max current rating of you battery? (This is the maximum current that it is designed to give) Because if you're operating near or at this limit then it's gonna struggle. It can deliver it for short bursts but will struggle to sustain it.
Please be kinder to your battery, give it a chance to perform for you, I feel for it, I really do. Try pas 4 or 3, it will knock a few mph of your top end, but will it increase you journey time much?