I'm so sorry to hear about your husband. But I do think people are right when they say it isn't your fault. I know it probably feels like even if it were your fault, people's politeness would prevent them from saying so anyway, but I still think they're right.
People ultimately make their own decisions in life. Your husband made his own decisions. It isn't a case of if you hadn't left he would still be here, there is more to it than that, the truth is if he hadn't made the decision he made and taken the action he took, THEN he would still be here. He isn't not here anymore because you split up temporarily, he isn't here because he chose to leave in the manner in which he did.
You obviously left for a reason, but you didn't leave with the intention of causing what has now happened. If you broke up often and always worked it out in the end, then your husband knew that as well as you did. If you broke up and made up before how were you to know what happened would happen on this occasion? Many people tell others they cannot live without them, either because they mean it in some sense or as a means of holding on to them and making them feel guilty, but that doesn't automatically mean they will carry things through in this way, and you weren't to know that he would.
Guilt is a natural reaction to the loss of a loved one and we all feel it even if our actions have no bearing whatsoever on an event. Whilst you are feeling guilty now, you will probably soon feel angry, first at yourself and then probably at your husband for doing what he did and especially at the time he chose to do it. This too is natural and to be expected after such a loss.
This website is really helpful - it's actually a pet loss website but it's descriptions of the stages of grief for loss and how you might feel at each stage I found really comforting. Just replace the word 'pet' with 'person' and it makes a lot of sense:
You WILL get through this but you should expect to feel guilt and anger because it's natural to feel that way but also because ultimately it sounds as though what your husband did was very selfish and the timing was designed to make you feel as guilty as possible. The timing may have been a coincidence but if it was it was a very unfortunate one. But you are not responsible for his actions and I hope as time passes you come to realise this. You are not the cause of your husband's death, his actions were the cause of his death.
I hope this helps.