Hi Claudia,
do you mean that the EAP-TLS authentication fails only on some 2960 switches and it works on other 2960s?
What is the IOS version you're using there?
What is the RADIUS server in use?
What is the exact error message you see on the RADIUS side?
Usually, the reason for the EAP-TLS handshake failure is to be troubleshoot on the supplicant and AAA server, however, there may be something on the switch depending on the certificate size and MTU settings on the switch(es).
What is the server cert size and the MTU configured on the switches?
With the info you provided it's difficult to say what's the reason of this failure.
I would suggest to start looking into the above mentioned topics, else you would need to proceed with deeper debugging and sniffer traces, which may be better/easier to handle through a TAC case.
I hope this helps.
Regards,
Federico
--
If this answers your question please mark the question as "answered" and rate it, so other users can easily find it.