A few months ago I counted all the users that have logged in at least once in the past month, and that had sent at least one card since joining postcrossing. My figure was around 65000.
A few of them didn’t actually send any cards in the past month, but are still active in the sense that they check the website occasionally.
I have a different theory regarding the slowdown: I think that a new-ish user will draw most of the time (depending a lot on their drawing patterns too) seasoned, reliable users - top users that are owed large numbers of cards at the time - so their cards will be registered promptly. As one goes into their thousands, one catches more and more often newbies that might have lost interest, people that are registering with delays, people from countries with slower mail systems and so on. So top users eventually get longer travel times and more expired cards per trimester.
And sort of a corollary - the ratio of very active, longterm postcrossers that joined in recent years is much smaller than those of olden years. I think it’s because if you’re a certain age group and postcrossing is something for you, you’re way more likely to have heard about it already by now. There are people still discovering it, and some will stay, of course - but it’s been almost 20 years since its launch, plenty of time for most people to learn it exists, and try it out if they are so inclined.