Switch Rebooting: How To Determine When You Are Remote

I got a call from one of my customers who had pretty much already figured out what was going on, but wanted me to look at it anyway.  It looks like the his Cisco switch was going down for some reason.  So I VPNed in to look and see what I could see.  When I tried to telnet to it, my session just froze up on me.  So, from the core switch, I simple ran a ping across to the switch (it was across an MPLS network).  Here is what I did to verify connectivity:
Core3560#ping 10.11.1.1 repeat 1000

Type escape sequence to abort.
Sending 1000, 100-byte ICMP Echos to 10.11.1.1, timeout is 2 seconds:
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Success rate is 96 percent (963/1000), round-trip min/avg/max = 1/10/67 ms
Core3560#ping 10.11.1.1 repeat 1000

Type escape sequence to abort.
Sending 1000, 100-byte ICMP Echos to 10.11.1.1, timeout is 2 seconds:
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Success rate is 93 percent (930/1000), round-trip min/avg/max = 1/9/59 ms
Core3560#ping 10.11.1.1 repeat 4000

Type escape sequence to abort.
Sending 4000, 100-byte ICMP Echos to 10.11.1.1, timeout is 2 seconds:
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I also decided to watch one of the IP Phones registration during this process, to verify what I thought was happening.  First when you could ping it, then when you could not ping it.