I don't think they're averse to third entries, but rather this is a byproduct of their business model.
Half-Life: They started out as a studio making singleplayer games, so making a sequel to this was straight forward. However, that game took so long they decided to overhaul the company into smaller releases. In 2015, a ton of people are required to make a AAA singleplayer game, and they seem to only want to work on games as a service, which doesn't fit very well with singleplayer gaming.
Counter-Strike: The follow-ups to this are mostly polishing up and adding to the same base game, but technically there's been 3 or 4 entries depending on how you want to count. They're probably not going to replace CS:GO anytime soon though since it's a service platform now.
Dota 2: This is only a 2 because they didn't have the original game, and it's a service platform now. It's a pretty new platform as well so it's not due for a replacement or refresh anytime soon.
Portal: They made a small experimental game with a team they hired when they liked their prototype. They then made a sequel to it because they had a variety of ideas for a full game. However, after that, they became notably more committed to games as a service, and the service component of Portal 2 didn't really work out, which probably helped get them the rest of the way off the singleplayer game path.
Left 4 Dead: They're making a third game as their primary game project. Maybe it won't be called Left 4 Dead 3, but it will unambiguously be the third game. It could plausibly be an f2p game, and it will almost assuredly be a long lasting service. Or, to put that in other terms, I'm not sure if there will be a Left 4 Dead 4 versus just updating Left 4 Dead 3 for a lot longer than they did Left 4 Dead 2, this time tying in ongoing monetization mechanics to make that more plausible.
Team Fortress: This was also a semi-experimental game that followed up on a game from ten years prior and was turned into an f2p service platform. It's possible they'll actually make a Team Fortress 3 as Team Fortress 2 is getting a bit long in the tooth even for a service platform and it's not getting a lot of updates anymore. Ten years for a service game is also about right in terms of how long you might wait before refreshing with a full technology overhaul, so we'd probably see it around 2017 if they intend to do a refresh. Either way, the reason we haven't seen a sequel yet is pretty straightforward.
I don't think they have any other franchises they'd actually consider continuing with. They seem totally uninterested in Day of Defeat, Alien Swarm was released because they hired the staff from the mod and didn't want their mostly completed work to go to waste, and obviously things like Richochet aren't even up for discussion.
