This has been a known ongoing issue, and is mostly referred to as the " invisible cars " problem.
(If you wanted to search the forum for that, you'd turn up threads dating back to GT5 discussing the issue.)
I don't know what exactly causes it, because the same people might not have the problem sometimes, and then other times they do.
So I'm skeptical about it being about the internet connection exactly. Usually internet connection problems cause lag (cars that teleport around the track).
It's almost certainly more about internet compatibility issues.
And does not seem to matter geographically. (ie: I have seen people who live in the same state in the US have problems with each other, and people across the Atlantic from each other NOT have problems.)
In general, it's often sorted by both parties (who can't see each other, or can't be seen), exiting the room and rejoining the lobby room.
After all this time, I'm still undecided whether clearing the cache has any effect, as just exiting and rejoining seems to help.
(I've also wondered if problems happen more when lots of people are joining the same room at once, and that's why rejoining helps.)
A hard wire connection from the internet (router/modem) to the PS3 is recommended, just generally, because it's more reliable. Just because doing it over wifi, there's more chances for interrupted signals.
If doing fixed host, you have to realize that if the host drops connection, the whole room drops. So hosts that choose to use "fixed host" should have a fairly reliable internet connection (speed isn't as important as reliability here), and therefore be on a hard wired connection.
I use a short cat6 cable from the router/modem combo to the PS3. I'm lucky in that our router is literally right next to the PS3 in our house.
