EG91-EX random SIM problem

Hello,
We are using the EG91-EX module (EG91EXGA-128-SGNS) in one of our designs, with SIM cards from Matooma.
Most modules have been working perfectly for months, but a few of them give us a CME error 13 from times to times.
When it happens, a software or hardware reset does not resolve the problem : the module reboots, but still gives a CME error 13 when we try to send data. The problem seems to solve itself after an hour, or after removing then re-inserting the SIM card.
Also, it tends to happen multiple times for a few weeks, then stop happening for a few more weeks.

Today, I have been lucky enough to be near a device with the problem happening. Here are a few oscilloscope screenshots:

Yellow: USIM1_CLK
Blue: USIM1_VDD

Yellow: USIM1_CLK
Blue: GND (on SIM card connector)

All the signals have been captured on the SIM card connector.

The most obvious thing is the low level which is not 0V but approximately 250mV.
About an hour later, the problem had disapeared, and the low level was back to 0V !

Has anyone ever seen this behaviour ? Do you have any idea on what could cause this problem ?

Best regards,
David