Funny that you mention it. Sony announced earlier this year that they would be shutting down the PS3 store permanently (including the ability to download past purchases), and only delayed the move due to public backlash. They did shut the PSP store though, so those games are unplayable now.
The email I got from Sony back in March said that they were only disabling new purchases, "You will still be able to download your owned PS3, PS Vita, and PSP content, including games and video content." Full text: https://paste.debian.net/1224883/
Now that they've backed down, I'm pretty sure you can buy new PS3 games as well.
You can, but they made it more difficult in that you need to add funds over the web or through a PS4/5 or gift card. Also that the prices now tend to be the original list prices which never go on sale but do for PS4/5.
