Trying to find a comparable relay

Unfortunately it looks like a custom rack for the relays making it difficult to sub, there are many N.A. relays that will do the job, in a pinch if you are sure the relay is the problem, I would tend to cannibalize the suspect relay and leave just the base with the plug in blades, from there I would wire new conductors out to a separate common relay.
I am assuming there is nothing really special about these relays, such as latching etc, an examination with the plastic cover off would show.
Does it show anything special on the schematic if you have it?
M.

 

It may be also best to check the nature of the load, if the problem is not a common one, something it is controlling is the problem?
M.

 

As an interim measure You could take the cover off and free the contacts and polish them up with 600 g paper.
M.

 

Minder brings up some good points.
From my experience, these pin type relays are garbage and don't stand up well. Particularly with inductive loads.
I would retrofit that board with larger and more robust relays. It will save you head aches in the future. You can add din rail sockets to make future relay replacement a snap. That said these relays should work with what you have now.

http://ab.rockwellautomation.com/relays-and-timers/pcb-pin-style-safety-control-relays

 

Not a bad idea to investigate wither suppression is warranted.
Eg. Add a Varistor across AC load if it's inductive.