What does tcpdump show when you try to ping and it fails? I think you have something on your network that is either doing proxy arp when it shouldn't or some device with more than one interface is set to bridging mode and then starts blocking traffic after the typical spanning tree intervals. Both are long shots, but tcpdump or wireshark will be able to help a lot more.
What does the /var/log/messages file say when the problem starts? Set syslog to log at a debugging level and check the file again when it happens again.