Alan,

the reason for the "insufficient memory" messages is very likely that the largest available contingous memory block is smaller than the maxtransfer size for the backup. The default blocksize is 4 Mb, but if your on SP3 or higher you can define a smaller blocksize in you backup statement.

See: http://msdn2.microsoft.com/en-us/library/ms186865.aspx

and http://support.microsoft.com/default.aspx/kb/904804

But even though changing the maxtransfersize might solve your problem in the short term, the real problem is not enough memory. If you can't add additional RAM I've seen instances there even the lowest value for maxtransfersize was too high. We ended up running dbcc freeproccache to free up memory. Yes it will hit your performance, but so does restarting the service.