Hi Petr,
You might be able to try disabling autonegotion if this is a Gig port. Autonegotiation is part of the 1000BaseX IEEE standard and is used to diagnose L1 issues. In this case, it's non-standard, so disabling autoneg could help.
If this is an IOS 4948
-> under interface
#Speed nonegotiate
A side note - typically with a SPAN monitor port, no traffic is switched from this port unless ingress keywords are specified. This means that even if the monitoring device did try to send traffic, it would be dropped at the port. This can be verified through the software configuration guide of your IOS version.
HTH
Eugene