Can excessive text messages stored on phone cause issues?

Can too many text messages stored on my phone prevent me from receiving new messages?

Recently I've had multiple people text me, yet I haven't received the messages. I checked the messaging log on my cell account online, and the incoming messages are listed, yet they never showed up on my device.

I spoke with T-Mobile tech support; he said that I had too many messages on my phone (5000+), and that the more text messages I have stored on my device, the higher the chance of an incoming message getting corrupted (that is, not received). He recommended keeping only ~200 messages on my phone.

Is that good advice?

He also said to restart my phone every night, which I'll start doing (instead of every few days), but I had never heard to not store too many messages, so I was curious if there is a technical basis for his advice...

I have an HTC One S (Android 4.1.1), and I am using the stock messaging app on T-Mobile (in the US).