I'm not experienced at all (I think I've been reading more about game-mechanichs at work than playing) BUT on my second game ever (tough difficulty, medium map, abundant everything except anomalies, slow tech, 4 opponents) I actually had my peace-offer accepted after a looong time waring. (long story of it is below)
I got a very nice starting world and only problem was that the yellow race (don't remember it's name now) was starting in the corner, so to say "behind me" in every matter. They had to crawl beside and through my budding empire to get some /lesser/ quality planets. I like to build my exonomy first in all games, so I happily built constructors for bases and the allowed traders. Problem with yellow was that many of his planets lay right beside mine (only they were of less PQ) which caused influence-friction.
In the diplomacy screen I then saw that the yellow started being hostile. I knew this could happen soon after the colony-rush, especially as my planets competed in influence with his in many places. So I built some very crappy small ships with no engines and max guns to scare them from declaring war. This seemed to work and I quickly (only a few turns to reach the top in the military "curves") went back to uppgrading my bases. (I can get greedy about wanting to max all bonuses....
Then "BAM!", yellow declared war and I had to scramble hard/long to change into producing very crappy warships (almost none of the slow research had gone into war before). I was surprised that I managed to get the upper hand (as I'm very new to this) in what was to become a long war. I offered peace several times but to no avail. I used alternating ships-tactics, if one got hurt it was sent back to a starbase to repair and if possible replacing it with another fresh undamaged, thereby loosing very few ships.
So I went on a really serious business of ruining his economy, killing off traders, troop-transports and single ships orbiting planets. I was amazed how resilient yellow was, I had thought my economy would go bancrupt much faster. But as I had killed off all his orbiting ships around half of his colonies for a few turns, I considered and started researching "Planetary invasion" just to get a stop to this endless micro-management of ships here and there.
It was by that time, but not having researched "Planetary invasion", that I by accident tried offering peace again and to my surprise the offer was green.