What Could Cause SMD Relay Burnout on Retrofitted PLC Output Cards?

Just so you can understand where I'm coming from, I was hired through the door into a maintenance position (lucky) and I've done what I can to learn on the job as well as at home. I come to this site today to gain more insight. This company has an older press that was retrofitted to use newer hardware (installed a PLC to replace the old controller) and now we go through output like crazy. But now onto the question.
A few days ago I came into work to find that 3 of the cards had melted together. After getting them out without damaging anything I decided to see what went on (trying to learn this job and understand what I'm seeing) and I noticed that one card had sever burn damage. An SMB relay appears as though it caught it fire or got hot enough to burn the PCB and melt the other cards. So I figured maybe a short in the device that the card/relay drives right? So I grab my multimeter and I tested for shorts as well as shorts to ground and I couldn't find anything. So what could cause the relay to burn up so bad if no shorts are present? The relays that we use to repair are the FTR-MYPA005D relays and the stock are the FTR-MYAA005D (the only difference I can find is the contact configuration). 

I want to reiterate that I'm not looking for someone to put me on a path to repair the press or the issue but I would like to understand what could cause this type of failure when everything I checked appears to be in good working order.

120VAC systemX20Do4649 Output Card
Let me know if there is other information that I can provide so I can gain a better understanding of the hardware that I'm dealing with.  I have provided the data sheet for the relays that we use for the in house repairs.

The SMB relays you are using have a maximum current of 5A. You say that you "go through output like crazy" What is the current you need to switch with these output relays?
I suspect, since this is a retrofit, that the outputs were not sized correctly to the load. Most of the time, a power relay will fail open or shorted. It's possible in this case that the part failed as a higher resistance short or that it caused an arc which burned the part.
My suspicion is that you need a bigger relay for this application but you may be able to find some arc suppression circuit that you can use to protect the relay.

Thank you for your time and reply. I can't move to a larger relay because of they are part of the output cards. When the relays fail I usually unsolder the failed component and replace it with the ones we can find. The company that retrofit the press sent us arc suppressors and told us to install them at each of the valves located all over the press to exclude any non-proportional valves. Do arc suppressors work best across the load or at the contact? I'm currently Googling this question.

I'd put the arc suppressors near the contact (which is where you have the arc). I'm guessing that it is primarily one or two relays that fail. If so, I'd protect them first.
If the arc suppression doesn't work,  you could suggest to get (or build) an intermediate relay circuit to go between the failing contact and the load. Or maybe you just buy a large stock of replacement relays.

Hi Chris,I think Elizabeth is on the money here. If you had the space in the control panel could you fit in a couple of  relays with contacts of a higher rating rather than trying to solder in larger relays. And then just drive those from the relays that are failing? It would save you a lot of hassle! And possibly solve your problem.

Hi!

I'm still learning all this on the job (so thank you both for giving me insights into the issue as well as remedies) and I will find out! Although I wouldn't see why it would be an issue. But then again, I'm the new guy roaming the internet buying books and asking experts!