I guess 2147483647 (0x7fffffff) is what it uses for Unknown when it is going to flood packets.
A central syslog receiver is one of the things that is likely to drop out of the forwarding tables on switches. The assumption is that traffic on a line is bidirectional, or at least acknowledged. If it troubles you, you can add static MAC mappings, or have the syslog receiver send a 'hello' packet every few minutes.