If you have received the 20 minute Leaverbuster punishment, that means you have been leaving/disconnecting from a lot of games, as that is not the first punishment you get. While it does suck that you have a Leaverbuster punishment from crashing, it sucks even more for the other four players who are stuck playing a 4v5 due to you crashing.
Now, if all of these leaves/disconnects the lead to your punishment are due to crashing, why do you continue to queue up for matches? You may not be able to control when you crash, but what you can control is when you queue up for games. If you continue queuing up knowing full well that you have been having problems with crashing recently, you risk crashing and ruining the game for your team. Doing that is your fault, and that is why Leaverbuster punishments are still given out due to technical difficulties. It's up to you to be able to maintain a stable connection, and if you are unable to do so, then you should stop queuing up for matches until you can. If you need to test see if something has worked, do so in a custom game because Leaverbuster does not care about those. You shouldn't be queuing up for matchmade games without out finding a solution/knowing if a possible solution has worked or not.
I'm not all that good with tech stuff, so I won't be able to offer much, but Riot does have a Troubleshooting guide on their support page if you haven't checked that out already. If you have and you're still having problems, then your best bet would probably be to make a post in Help & Support or possibly make submit a support ticket.
As for reducing the wait time for the punishment, it is already possible to lower the timer. However, it's not based on how many days have passed since your last punishment. It's based on how many games you play without leaving, disconnecting, or otherwise being marked as AFK since your last punishment, and the number of games it takes to lower the wait time is a lot. The exact number is unknown, but when it happens, you will receive a message stating something along the lines of "hey, we've noticed that you have been leaving less games recently."