Recommended rejection of a paper, but invited to review the paper again I was recently asked to review a paper, and ended up recommending a rejection of the paper. The journal has, apparently, asked the authors to revise their paper, and the journal has come back to me asking me to review the revised paper. There is, however, no option offered for me to decline. I will likely recommend rejection again as I see that the main problem with the paper is still not addressed. What should I do in this case? Should I write to the journal that I am not willing to review this paper again, or should I go ahead with the review and recommend rejection for the second time? Since I need to provide my comments to the authors again, what should I write while still being constructive? This was my first time recommending a rejection.
This has happened to me a couple times. As Peter Jansson has pointed out, what probably happened is that, while you recommended rejection, reviewers 2 and 3 said "it's actually publishable if the authors solve such-and-such problems". This is the kind of situation where a sympathetic editor will make a "revise and resubmit" decision. 

In this particular case, you have it easy. Just write a very short review along the lines of "in my first review, I recommended rejection of this article because of [problem that made you recommend rejection]. As the authors have not addressed this problem, I'm regrettably forced to maintain my previous evaluation".

[FWIW, one of the times I reviewed a paper like this, the journal actually ended up publishing the paper in question, with the problematic section still exactly as it was  when I reviewed and rejected it. Go figure]