After watching the "feeling" status for a few games, I have noticed the following.
1) Usually only 1 empire will turn on you gradually. For me it was the 2nd ranked empire. Nothing, free resources, tech, releasing claims to systems (I did not try giving away planets

) will stop them from turning on you.
2) The remaining empires continued to stay friendly while the 1 grew less friendly. Once the first declared war, the rest followed suit within a turn (maybe 2). I also could not stop this from happening.
I have not encountered any empires after war was declared, so I do not know what their response will be.
Also note that some of the empires that went to war with me had no "official" contact with the other empires. Nor did they during the war(s).