First, I have found out that my provider is dropping the connection after 30 minutes.
Then, I think that pppd was failing to reconnect, because I had set the ppp0-interface to use a PIN-code for the SIM-card. After disabling the PIN-code on the SIM-card, pppd does reconnect automatically.
It seems, that pppd only transmits the PIN-code to the SIM-card the first time it connects.