The latest increase attempt came last week. This is likely to succeed since Southwest has actually hopped on board. When Southwest goes along with it, others generally follow quickly.
But there's a trick to these airfare increases. They never include sale fares. Any advertised sale fares can't increase until the advertised period is over, but in general they don't see big increases anyway when demand is low. Sales are meant to stimulate traffic, and right now, the airlines need more traffic despite all the capacity cuts.
Yes, airlines need to increase their fares as well considering how far yields have fallen in the last year, but there's a reason they've fallen. Demand is weak. And raising fares will nearly always result in demand going down. So what will happen when demand drops? More sale fares will have to be pushed out to fill those empty seats.
So while airfare increases may be good for the airlines on one hand, it may also result in the necessity for more fare sales in the future if demand doesn't strengthen.