I tried to find a "delete build history record" but I couldn't find one. That doesn't prove it isn't there, but it it was, it would be an opportunity for devs to abuse it as some PM's use the history as a metric that may say something about code quality. If we could delete all the failed builds, it would make this statistic game-able.
Of course there is the policy page which has some tuning, but not the sort you mentioned (you can't remove just failed builds)
admin/cleanupPolicies.html
You might want to pin your favorite builds (which should protect them from clean up) and then change the policy to clean up everything 1 day old, then change the policy back to something more reasonable.