In the past, the insecurities flare when I feel that there is a cowboy out there who is determined to end the relationship I have with someone.
How I deal with it? By increasing my trust and confidence in my relationship to the point of knowing that no cowboy is going to be able to cause that to happen. I tired that in my previous relationship, but she tended to be someone who lived her life on a whim, in spite of saying that she wanted stability - this didn't help me much - and the end result reinforced exactly what I feared - someone else came along who wanted to be monogamous with her and she followed the shiny and "jumped ship". It didn't last terribly long, and I hope she feels that it was worth it. (Me? Bitter much?)
My current two are very consistent - their actions reflect their words and their words don't change from day to day. They have had their fair share of approaches by cowboys but haven't been interested, and this has just served to help lay my insecurities to rest quite a bit. I am very open about these insecurities with them, and give them feedback on how I am feeling. They, in turn, both do their best to help me through when the demons come howling.
"Listen, or your tongue will make you deaf." - Native American Proverb