Can SQL Server's crash resilience be improved?
I am aware that SQL Server is not designed for such scenarios and the correct solution is to fix the cause of the power loss […]


Actually it's designed to deal with power loss, that's why there are things like write ahead logging (WAL) and crash recovery upon startup (or whatever you want to call it). One of the ways this is done is by choosing to not cache writes which it seems is what the tablet is doing, hence the corruption.


  Nevertheless, are there any tuning options in SQL Server that I can set to reduce the risk of database corruption on power loss?


No, SQL Server is doing what it should. You should look either outside SQL Server (windows settings for drive caching [which SQL wants to be off but we can't force you], hardware/firmware updates, etc.) or as Eric has said, buy an external power supply for relatively cheap which could solve the symptoms (the actual issue is probably some type of caching or battery backed write that isn't actually backed).