What's the point of staying in an arms race? Sooner or later, most participants will fall behind for a while, and if the other party is really aggressive this will likely prove the arms race efforts to be a failure.
An arms race with a big portion of capabilities which serve more on the strategic defence than on the strategic offence could be considered as an excuse. The problem with this is that it's simply not describing post-19th century arms races well. Fortresses are not efficient enough any more.
So maybe arms races -once started for some reason- are being sustained by uncertainty?
Being just a bit weaker and thus capable of demanding a high price for aggression (maybe even win despite initially smaller military power) might explain why arms races exist and do last a while. The temporarily inferior side accepts its temporary weakness and just doesn't want to fall behind by too much?
Yet, how could this be? A rational inferior power would rather yield than to fight a damaging war and accept the near-certainty of defeat. The supposed exacting of a price would be a bluff. To fight a war from a position of weakness is kind of like betting your left arm in a poker game when you only have a pair of deuces.
Yet maybe it's the expectation that the inferior power will indeed follow such an irrational course (=not bluffing, with exact cards unknown to the other 'player') of action which preserves peace.
This would be quite ironic, for there's a substantial amount of irrationality in play when wars are being prepared or actually waged, too. It's almost impossible nowadays to get a good return on war efforts (save for wars of independence or special interests) and justifying the huge expenses in peacetime without an actual conflict on the horizon requires even more irrationality in my opinion.
Still, irrationality may preserve peace at times, which should influence one's judgement of seemingly irrational leaders at times. An irrational leader of an inferior country may serve the preservation of peace, while the same leading a superior power may be a threat to peace.
By the way; I'm still unsure why arms races exist(ed) at all. There are scores of examples where one side simply stopped playing along and dropped out of the race, with no aggression occurring afterwards. See Greece-Turkey or the South American dreadnought arms race for obvious examples.
Similar stuff years ago, and more specific to nukes:2009/03: Nuclear deterrence: It depends!