Disclaimer: if you (OP or someone else reading this) have suicidal ideations then please get professional help.
We find ourselves existing in the universe. If we accept the standard
scientific evolutionary view, we are all replicators. The only reason
we are here is that self-preserving physical matter, out of the set of
all possible physical matter, will tend to maintain itself in a
physical substrate over time. To commit suicide is to reject this
natural heritage, the only heritage that has allowed our existence.
Careful, this is teleological. It's not at all clear that we should (especially in this manner) talk about evolution like that. In other words: evolution can't provide existential reasons. We don't reject some sort of heritage because if we commit suicide then this wouldn't contradict evolutionary principles. Instead, it would be part of them.
For example, we could think of it like this: let's assume that some genetic variation leads to a higher probability of depression. Depression then would lead to a higher probability of suicide. A higher probablity of suicide would lead to a lower number of inheritance of the trait. This of course wouldn't mean that we shouldn't combat depression. But instead, using therapy to combat depression would also be part of evolution, in that it would maybe decrease the probablity of suicide.
Is there a sense in which the portrayal of suicide as this kind of
rejection is a cogent argument against it?
I don't think it's a good idea to try to get normative principles out of natural processes in that way. There are, of course, many other good reasons to reject suicide in general.
This gets perilously close to 'the universe has kept us here so the
universe clearly wants us here' or perhaps more tautologically 'we
exist to be here'. These are something like summaries of the idea I am
trying to elucidate, though the former carries some mystical
connotations and might be uncharitable.
"We exist to be here" is not tautological. "We exist because we exist." would be tautological. But the former gets some sort of existential reason from somewhere.
If we argue that evolution explains why we exist then I'd argue that this commits an equivocation. The meaning of "why we exist" would be different in that explanation which is why it doesn't work.