There’s that joke graph about “happiness in the life of a thanksgiving turkey”, where things are going amazingly right until a straight drop to zero. It works “right now”, up until it doesn’t, or there’s an outage that you can’t recover from, or some bad code wipes prod and your backups are useless (in this case likely nonexistent).
It also sounds like it isn’t really working even right now - from what op claims the productivity is not at all able to meet the deadlines being imposed by upper management. Death by competitors moving faster with a better product is a real thing, and if the tech stops them from doing so, that’s a problem.
The best strategy probably isn’t a rewrite, as others have suggested, but “don’t touch it if it works” is frankly an irresponsible strategy.
I’ve worked in a team where poor core tech (along with a sort of emporer-has-no-clothes situation where upper management found it politically impossible to acknowledge the issue) directly killed the profit, although this was in the market making space which has a much more direct reliance on technology. they got into their situation with exactly the attitude of “if it works, don’t touch it!” and basically stayed still while the competition flew ahead of them. Their product “worked”, in that it did what it was supposed to, but iteration on quality of trading and strategies was next to impossible.