Can two arms-racing species be stabilized?
To rephrase Cort Ammon. It depends on how you setup the system. 

Imagine each combat strategy as a point on a landscape. Good strategies are on higher ground, poorer strategies are on lower ground.

A and B each have their own combat strategy and thus start at different points on this landscape. Mutations allow a species (say A) to explore the strategies around its starting point. Selection will cause the curtail that exploration.

If A find itself on a slop of a hill, selection (ie your combat and mating system) will cause the A population to drift upwards on this slop. However if A find itself on the peak of a small hill, it has no where else to go. 

So how the scenario will play out will depend on the initial start conditions of population A and B. The mutation rate/genetic variability of the population (ie how many strategies population can explore around its initial strategy). 

Additional factors is the genetic system that you have. If individuals of your species can only have one strategy (haploid), the species will be bound to its local hill. However if an individual can have more than one combat strategy at a time, (ie a diploid or gene duplication in RL), then the individual can have a combat strategy that work (local peak) and have a second strategy that is free to evolve... free to explore the landscape... going down valleys of bad strategies... and may eventually find the foot of a mountain... which a peak fitness higher than even the local peak it started.