Well... it's not an easy question to answer, because you're getting into the guts of the simulation there. A few things.
1. As a general rule, your Influence with races only changes when you specifically take some sort of action. There are a few rare cases -- mainly hostile alliances -- where your influence will passively fall if it is above a certain total amount, but that's it. This is a mechanic that is designed to be managed like a resource by you, and it informs a lot of strategic decisions, etc.
2. Races, on the other hand, have all sorts of contextual reasons why their attitudes toward one another shift. Looks like 47 factors at present, although it keeps growing. This is not a resource, but rather is a part of the underlying AI -- as AI races react to one another, different influence factors get added (positive ones and negative ones), and it's a matter of which ones win out the most in terms of how they ultimately feel. If two races are at war, and you keep adding positive attitude factors between them, the war will just keep dragging it down, for instance. So there's nothing you can do in cases like that.
3. There is NO way to have an unwinnable game without it giving you a game over. In the literal sense of "unwinnable," anyway. You may have a game where "every battle I try kills me," and that's an unwinnable game, sure.
And, okay, if a hostile race controls 7 planets and the one ally you have left is unable to mount a defense you are
probably assured defeat (but doing something clutch like getting God Mote researched would turn that around in a hurry, actually). But in terms of the overall strategic scenario, there is no "hard lock" situation where conditions literally say "there is nothing you can do, period, in terms of options."
4. If everyone but two races are dead, and the federation is not formed, and they hate each other, that's one of those "you are probably going to lose" cases. There's likely a huge history of war and bloodshed behind that, and trade deals or whatever aren't going to overcome that. And they're probably actively at war at the moment. But even so, there's hope that you could pull off some sort of unusual thing in specific circumstances. I can't think what, but people are clever.
5. If you have a "federation of one" where the federation was formed but all the races are dead in it except one, then you can still win the game just fine by killing all the non-federation races. As long as there are no non-federation planets and there is at least one federation planets at the end of the game, you win. That could mean 7 glowing molten rocks, heh.
6. In general, that said, races can hate one another but still be in the same alliance. They won't break it off for that reason alone. So just because Race A hates Race B, if they like Race C and you can get C into an alliance with A, then you can get B in there by getting them to join C despite their dislike of A. Or if they like YOU enough, and the federation already exists, and they're not one of the really nasty races that just won't deal with you directly much, then you can get them to join simply based on their liking of you. Or there are some other edge cases, like showing military might to the Burlusts, and forcing them to join out of submission.
7. Influence is one of those things that comes and goes. It is something that you're not going to be able to keep a high value of for all races. So if you can't form a federation with the races that are spacefaring, but you're ready to do so, then smuggling spacefaring to another race and paying the piper for that can be a good move. You'll then be dealing with the fallout from that decision for a long time, sure, but basically you are going to be making some enemies in almost every game, so you kind of have to pick them.
8. Alternatively, don't forget that one way of "waiting" would be to run a number of dispatches and just make sure the solar system doesn't explode in the meantime. There's not a need to just sit around or something, you can certainly blitz through time really fast. There is a COST to that in a gameplay sense of "whatever happened while you were off mining resources or whatever it was," but it's not a literal time cost to you in terms of "wait for 45 minutes," which would be agonizing.
And now, a list of some things that can help attitude between races:
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Pity: certain races feel pity towards other races that have really bad circumstances, primarily a negative birth/death ratio or a bad racial compatibility with their planet. This mostly applies to good races, though.
Positive Coup: you can't really control this, but sometimes and event will happen that makes the attitude of the new government have shifted attitudes up (or down).
Wellbeing Admiration: If someone has really high RCI values, then most other races will admire that and like them a bit better over time.
Friend Of My Friend: This mostly applies when Race A really dislikes Race B, but both like Race C and vice versa. In that case, A and B would become a bit more neutral to one another, gradually, but it would never make them really in love.
Grateful For Technology: Tech gifting.
Commerce Partner: Trade routes between races improve attitude every couple of months.
Founding Partner: When two races are party of the original founding federation, that forms a certain bond.
Fuzzy Pacifism: If the thoraxians contract The Fuzz, they start getting nicer to everyone for a while.
Happy To Assist: When one race helps you and another race clean up AFA or pirates, then the races that work together can get some happy attitude toward one another for that.
Heard Rumors Positive: This is one of the special powers of the Boarines, particularly when Solar Unity is their priority (via having really high RCI on the planet of the regent you are dealing with). Encourage Relations between two races is really useful, and leads to this.
They Like Us: If Race A likes race B, then Race B can't help but gradually like them back a bit. Although if Race B hates Race A, then A can't help but dislike them back a bit. So both drift toward the middle a bit.
Joint Federation Membership: Being in the federation together causes a gradual increase in attitude over time.
We Need To Stick Together: If there is a "scary non-solo alliance" out there (Solar Axis Pact, Union of Independent States, or Trifecta of Superiority), then other races that are not in that alliance and who have kind of low-neutral attitude toward other such races will become more high-neutral in attitude, gradually.
There are maybe 8 other factors as well that are positive, but they are super specific and not something you can control, so I didn't list them.
Hope that helps!
