How can I make a failing relay more reliable?
Relays have a life span which is mostly determined by how much current and voltage the contacts are switching (and the inductance/capacitance and surge current) and how often they are called upon to switch. Increasing the coil voltage is unlikely to help if the contacts are worn out. 

Below is a curve showing the life span of the contacts for a common old-fashioned plug-in relay. As you can see, 200,000** operations is a typical lifetime at full load of 15A resistive load, and that will be shortened considerably if there is much inductance in the load circuit. Motors, transformers and indandescent lamps are particularly bad because they have a surge current on closing and/or arc when opening. 

** In Japanese (as in Chinese) the character for 10,000 (万) is more common than the character for 1,000 so \$10^4\$ shows up more often than one might expect. 



I would be tempted to try to McGyver a replaceable relay into your potted unit but without more information we can't really comment on how feasible and safe that might be. Note that sealing relays up 100% is a bit of a mixed bag. Many power relays have ports that are intended to be opened after soldering and cleaning, to help reduce the amount of crap that builds up as the relay contacts open and close. 

There are other things that can be done to increase the life span of a new relay such as making it open faster (and opening that port) or suppressing load surge voltage and current, but once it's worn out it's gone.