Hello Ray,
When Carver produced the very first caravan mover, they demonstrated it at the at the caravan show. It was fitted with an 85AH battery which was only charged overnight. The battery was more than capable of providing the necessary peak current but also the total power for the day's demos.
Now there will have been some differences between demo unit and your caravan, the demo unit was probably much smaller and lighter than your caravan, and of course it is a different make, but in essence it shows that the smaller battery should be able to cope with most real demands.
I do not know the details of the Titan mover, but as a general bench mark movers are normally expected to be able to move a caravan up a 1:4 slope.
I assume from your post , the mover actually stops turning when you breach the critical point on your ramps.
My first suggestion is to check you are not asking the mover to do more than it is designed to do. Just because it moved your previous lighter caravan over the same obstical, does not mean the obstical is less or equal to the design spec.
Secondly; are the tyres are correctly inflated, and the mover correctly positioned. If the mover is too close to the tyre, when the mover is engaged it may be pressing into the tyre with too much force, and that may be adding friction to the movers bearings and impeding its operation which will show up on high load manoeuvres.
Failing that, perhaps the battery is not as good as it could be. as batteries get older they loose performance, both the peak current they can deliver and the total charge capacity. If a battery has been abused (e.g. left discharged, or asked to deliver more current that it is designed to do, run out of electrolyte, left on high charge for too long etc) then this will also impare it performance.
What ever the reason, I am sure its much easier than trying to push teh whole caravan by hand.