Can't connect to iMessage on my iPad

Hello,

I'm currently having trouble with iMessage on my iPad 2 running iOS 9.2.1. iMessage used to work seamlessly before a couple of week ago, when it asked me to enter my Apple ID. Since then, I have not been able to connect again to iMessage on my iPad. The attempt lasts a couple of minutes, then tells me the iMessage server could not be reached. iMessage works well on my iPhone and MacBook, though.

The thing I have tried are :

• restoring my iPad --> No change
• Reset network settings --> no change
• Log out of iCloud and log in again --> No change
• use another Apple ID for iMessage --> I succeed to connect to that Apple ID. I then tried my usual ID, connection succeeded, but 5 minutes later, Messages asked for my ID again, and since then I have not been able to connect to either account.
• I checked if time setting was on Automatic --> it already was

I'm running out of ideas to try and make iMessage run again on my iPad, and I'm looking for people with a similar problem (or even better, a solution).

Can someone help me please?