In about 95% of crashing cases, memory management is what kills things.
Apple was traditionally better at memory management than Windows (primarily because Apple is based on Unix, which historically managed memory better). But there are all sorts of app developers that are lousy programmers and don’t do memory management particularly well.
The reason why shutting down the iPad is ineffective is that before shutting down, the iPad caches memory, meaning that when you turn it back on, the device just reinstates things to how they were before. So you are perpetuating the problem, not solving it.
The only way to address this semi-permanently is to wipe the iPad and reinstall / redownload everything. In other words, go back to factory settings. The reinstall your software.
That will fix things for a while, until another poorly written program starts eating up your memory.