The thing is, you can't fight 24/7. What prevents you to have other things along too? I'm really pissed off with Whedon's lack of explanation here. And I'm not buying that it's because Steve is 100 years old, he's actually not. He has lived only 25-30 years in terms of actual life. What was Steve's problem with Peggy here? She is almost a soldier herself. Basically, Whedon made them not much better service, than Brutasha. And Steve "healing" with Sharon's "love" would be an assassination of his character for me.
Steve may look like a 30 year old man but he's not actually 30 anymore. He even acknowledges that in Captain America: The Winter Soldier and what has prevented him from having other things besides being an avenger? How about the fact that he still feels out of place in a futuristic setting and he's lost everyone from his past life (except for Bucky). Even after he's been thawed out for 5 years, he's still a foreigner from a different timeline whose been thrusted into the 21st century and he never really had any time to adjust due to too many obstacles like a crazy demigod, alien armies, killer robots, an old friend turned brainwashed assassin, and the return of HYDRA. As for Peggy, Steve doesn't have a problem with her but she's an old lady now and chances are, she'll pass away in Civil War so once again, Steve feels that it's too late to find love and happiness.