I have to agree with 'thinkpads_user' you need to ascertain exactly where your drops are before you can move any further.
once you know where you are getting the drops then you can make an assessment of what contingency you can put in place. You might find you can install a back up connection for that 'leg' of the connection and fail over to this using a firewall rule if that legs drops.
you could always put in place a cheaper DSL or similar connection as a backup to manually fail to if you get a long (time wise) drop out.
Another option for the intermittent drops could be some network cacheing equipment which may improve the user experience over less stable connections. something like a riverbed or citrix wanscalar maybe help...