Wouldn't it be more likely to stay lit if it didn't have ash since it has more access to oxygen.
If you accrue enough ash to choke out the ember that would definitely cause it to go out but I don't own a bowl big enough to get that much ash. It seems to me that to a point ash retains the ember's heat and helps focus airflow similar to the way putting your hand/fingers/tamper over the rim of the bowl while taking a puff causes the ember to rapidly heat up. Which led me to conclude that a little ash is always good and helps it stay lit. However, I think it is absolutely possible that restricted airflow due to excess ash could shorten the life of an ember but whether that shortening is exceeded by the increase it receives by the insulating effect of a moderate ash layer is open to debate from much more experienced pipe smokers than I.
I would dare say that, in my opinion(garnered through my admittedly limited experience), as long as you aren't dealing with an overly deep bowl in excess of several inches, or a deep narrow pipe like a stack, you won't have to worry about ash causing your pipe to go out. But I have found that not dumping some of the loose ash at least once or twice in a moderate sized bowl will cause the tobacco to burn too hot and negatively effect the flavor and enjoyment of the bowl if I am not careful in the vehemence and frequency of my puffs. In any case, when I deem my new pipes "properly caked" and stop retaining all the ash till the end, it tastes and smokes much better. Also worth noting, even while performing my voodoo break-in ritual, the only times I have trouble with relights is due to overpacking or packing overly moist tobacco. But that may be due more to me being an inherently fast smoker that actively works on cooling his jets and letting it sit a bit longer between puffs. I had a Patience a long time ago but I was in a hurry and got sick of waiting on it so I threw it away, for the life of me I can't remember where. Pipe smoking has forced me to try and make a new one.
With all that said, your experiences/methods may differ drastically from mine and I am quite sure that the OP would appreciate and benefit from an account of both yours and mine.