@Rosalie15 This has happened to a lot of hosts at some point. It happened to me about 2 years ago and I reported it and they took about a month and a half to get my text alerts back up (which I really rely on). First they made ridiculous suggestions, like maybe my text inbox was full (Uh duh, don't you think I'd have made sure that wasn't the case before bothering to contact CS?) , then said it must have something to do with my phone provider. Anything to avoid actually having to admit it was their tech issue, which they finally did. In the meantime, I just had to check my airbnb account a couple times a day so I didn't miss anything. I was still getting the email alerts, but that meant I had to open my email- so much easier andfaster to get the SMS alerts.
You've tried uninstalling and reinstalling, unchecking the box and rechecking it, so now your option is to contact Airbnb and report it, make sure they understand you rely on these, and hopefully they'll get them up and running for you again sooner than they did for me.