Recovering from a consequence usually has no penalty for failure. It's an overcome action, and failure at an overcome doesn't come with a penalty. If something was opposing you somehow, though, they'd succeed, which would probably be bad.
As for whether you can attempt recovery multiple times, the rules are silent. They won't provide an answer to this, because you need to look at the narrative for your answer.
In your scenario, it's naturally not going to be as simple as just a Consequence and a Lore check: someone has a wound, and someone else is performing surgery. Someone has their confidence eroded or they're intimidated or horrified, and someone's giving them a pep talk to snap them out of it. Someone is totally hyped up, and another person's trying to get them to calm down.
So when you're dealing with this circumstance, derive your answer from the narrative:
- Can you really perform surgery safely this soon after the last attempt? Do you have the time to wait for them to recover first? Do you have sterile equipment available?
- Will a second or third pep talk actually help? Does anyone know another way to snap them out of it, and will that be helpful at this point?
- If the tried-and-true method to calm that person failed, does anyone actually know another way to de-hype them?
If you can say that yes, this second attempt to aid in recovery will be legitimate in this narrative, then go for it. Otherwise, probably don't make another attempt.
After all, by the Fate rules, we could all just roll our Overcome attempts several times until we get a good result, but narratively that wouldn't necessarily make any sense at all, and probably isn't good for the drama that makes Fate so fun.
If the PCs want to enable this second recovery attempt but the narrative's presently not allowing for it, they can use Create Advantage to change the context so there is justification to try again: find some Fresh tools, fish out A good book or A gameboy, summon up The iron will of a drill sergeant, or so on. You'll simultaneously get free invokes to pass to te roller so they're more likely to succeed.