Just yesterday I started using the PBE, I played a few games without any problems. Today I attempted to play a game only to be bugsplatted during the loading screen, I tried to reconnect several times, but the reconnect button only closed the League client and did not bring me back into the game(luckily my team managed to win 4v5). So I was unable to rejoin this game and received a leave. Later I was playing a game and at about 20 minutes in we 100% sure we would win the game, but then I receive another bugsplat. This time I was able to reconnect, but between re opening the client and a pretty long loading screen it took a few minutes. I got back just in time to see my team destroy the enemy nexus, but as soon as the game ended and we got to the post game chat I got the message that I was banned for ditching my team.

The ban is only one day, but at this point I'm probably just going to quit the PBE because this will probably keep happening

Anybody else had problems with bugsplats/ is there anything I can do about them besides report them after they happen? Is it considered the players fault for bugsplatting?

I had something similar today, except, I only managed to load 1% before bugsplat. I haven't been punished yet but it wouldn't surprise me if I was. Also, it bugs me that I am now -5 points (it was first game) because the client was pushed through as unstable this patch.

I understand PBE is beta and we're here to find the bugs, but, disciplinary action for finding the bugs seems like it needs to be reviewed.

I understand that it is frustrating to receive a ban for leaving a game, because of a game crash and we definitely don't want to punish users for malfunctions of the client.
We have leaver buster active on PBE and it's bumping lever levels way faster than the normal server, so with relatively low amount of leaves you can get a ban. We decided to configure it that way in order to deal with people who systematically and intentionally leave games.

What I would advice you to do is to reinstall your client and in the future if you experience bugsplats, repair/reinstall your client and check if the crashes are fixed in a custom game.
This way if you still continue experience crashes you can let us know that something is wrong on our end, without receiving any leaver penalty or harming the experience 9 more players.

I will try to re install the game then

How do the punishments work in games like the one where I reconnected? Does it count as a leave if you're gone for a certain amount of time regardless of whether or not you come back?

I've had similar issues with Live. I've had several games crash (sometimes 3-4 times in one game) because of bugsplat reporting. Luckily I was playing with friends those games and they didn't report me.