Either the communication to your remote db is not ok, or the rows (better to say specific rows) contain too much data. Try increasing the wait_timeout or max_allowed_packet setting of the remote db.
max_allowed_packet is all right unless you strore huge blobs in the Access db, but I was not talking about connect_timeout, but about wait_timeout. wait_timeout being 5 secs would be a way too short period!
I would increase the wait_timeout setting! My default value is 28800… About max_allowed_packet: find the largest row in your Access db (the row that contains the most data), determine its size in bytes and compare this value to the max_allowed_packet. If the size of the row exceeds max_allowed_packet, then increase the setting's value. Otherwise you can leave it as is.