As per the comments on your question, I think this is really context specific and the role of an author can vary quite subtly from area to area. I'll try give a general answer to the general question first, and then look at the specfics of your case afterwards.
How to handle not being credited for research software development in papers?
The first question is whether or not you should be credited for the software you developed in the paper. The answer is predicated on what precisely the contribution of the paper is and what the contribution of the software is.
If, for example, (part of) the core contribution of the paper is describing optimisations and techniques that you invented and applied in the software, then I think it is more than fair that you should be credited as a co-author.
If, for example, the core contribution relates to a methodology for doing X where your software was specifically designed for that methodology, then you should probably be credited as a co-author or, at the very least, mentioned in the acknowledgements.
If the core contribution of the paper is not directly related to the software itself but the software is used to some ends, then you should probably not be credited on the paper (otherwise Linus Torvalds would have millions of publications). But if the software system was described in another paper and played a significant/specialised role in the current paper, you could expect a citation.
Since the publications wouldn't be possible without the systems I developed would I have any remit to ask for credit and/or authorship?
I think your reasoning is a little flawed here. Making a research paper possible does not entitle you to co-authorship (as a simple counter-example, if paper A builds upon the results of paper B such that paper A would not be possible without paper B, the authors of paper B should not expect co-authorship on paper A). Providing part of the core contribution of the paper—the reason why it was accepted in the first place—entitles you to co-authorship.
I noticed something crucial in your comments that you didn't clarify in your question:
"Since xxxx our system has collated data on x cases and found that.."
The authors should absolutely not be claiming credit for a system they did not design or build. This is clearly wrong. (And it also indirectly suggests that part of the contribution is indeed the system and the authors are trying to claim credit for it.)
Since you know the authors, you should talk with them, show them the relevant quotes in the papers and tell them that you are not happy with them claiming the system as their own. Tell them that if they wish to continue claiming the system in future then you should be a co-author on the paper.
If you wish to escalate, you can contact the editor(s) of the journal(s) involved and tell them your story. The editor(s) might agree to let you publish a letter referring to the specific paper and outlining your case. This should be considered the "nuclear" option.
EDIT: Not in answer to the question, but this quote in the transcript of Hamming's address "You and Your Research" (well worth a read for anyone in research) reminded me of this question:
I also did a second thing. When I loaned what little programming power we had to help in the early days of computing, I said, "We are not getting the recognition for our programmers that they deserve. When you publish a paper you will thank that programmer or you aren't getting any more help from me. That programmer is going to be thanked by name; she's worked hard." I waited a couple of years. I then went through a year of BSTJ articles and counted what fraction thanked some programmer. I took it into the boss and said, "That's the central role computing is playing in Bell Labs; if the BSTJ is important, that's how important computing is." He had to give in.