Invalid memory alloc request

On systems running Postgresql 8.3.6, I have a nightly backup using
pg_dump that failed on two machines overnight with this error:

pg_dump: SQL command failed
pg_dump: Error message from server: ERROR:  invalid memory alloc request size 1376006425
pg_dump: The command was: COPY public.tablename (ts, fn, data, textdata) TO stdout;

The two machines where this occurred have similar, but not identical,
data in this table.  Both machines are running FreeBSD 7.1 amd64.  I ran
a query "SELECT SUM(LENGTH(data)), SUM(LENGTH(textdata)) FROM tablename"
to sum the length of the data and textdata columns (both of type bytea)
in this table, and the results were around 140MB for the data column and
500MB for the textdata.

I have seen reports of "invalid memory alloc request" errors in the mail
list archives, but those were considered likely to be file corruption or
memory errors.  Since this happened simultaneously on two separate
machines, I would not expect these issues to be likely causes.

Any suggestions?

Thanks,
Guy Helmer