I am nearly 60 now, dating in real life and online, so this post is me, looking back.
It might help to understand things by looking at it from two points of view OP: the social reality and the individual and personal view.
The social "reality" already referred to by some. By one's 30s, the fact is lots of "relationship" men will be - guess what - in relationships! Though I do think 31 is very young from where I'm standing! Anyway, the pool of men available to "be in" a relationship is, inevitably, getting statistically smaller. There are other social factors mentioned by others that also limit women's choice e.g. the age issue - men seem to be able to date almost any age. Whereas women commonly come on MN to almost apologise if they are 6 years older than their 28 year old boyfriend fgs. (It is of course nice that in public life anyway, there are exceptions - Joan Collins, Julie Burchill, Vivienne Westwood, women full of vigour and talent it must be said who also have a wide social mileau - who marry men much younger than them).
But there are also lots of individual variables, so I don't pay too much heed to all the posters who say they left Bloke A who was horrible and soon met Bloke B who was fantastic. Who these women are and what they want in a relationship may be v different to me. In my own case, I don't think I really wanted children or domesticity when I was young, or even when older, if I was honest. Perhaps I was damaged by some of my childhood which also made me "different" (though this understanding was hidden to me, probably others may have picked up on it). I liked good looks and intelligence in a man (though never interested in status or money) and this made the pool even smaller, lol! Perhaps also on an individual level, there were also other things against me [I could fill in quite a few things here, both positives and negatives] So, what I am trying to say, is there are many variables that may exist that make it more or less likely for you to meet "your match" if that makes sense. Most of them you won't have much control over IMO. Understanding this might also help you.
My only "advice" OP is to live life as fully as you can as a single person first and foremost. Whatever adventures or whatever paths in life you want to take, to take with both hands. I know you are a single parent which, unless you have support, limits things in some ways, much more if you are really on your own. But I really do think that trying too hard to pursue men can end in all kinds of weird scenarios. Keeping a dating profile up long-term might be useful, as you never know who drops by, but I wouldn't bother being too active or too over-excited if you get some male attention from that quarter (IYKWIM). Just take it slow and easy. Someone may turn up, someone may not. Something may happen and something may not. Try to enjoy what you're doing in life and accept and believe that your life has value with or without a man. My life has been hard as a single parent in some ways, but its hard to see what a man would have added, unless a true match had appeared on the scene and he never did.