Seems like a possible solution if the Martian atmosphere is humid enough. Maybe NASA will test it out on one of their upcoming Mars missions.
I'm thinking that since you have to dig down to even find a trace of water on mars, the atmosphere is likely bone dry. So, unless the dust has its own built in adhesive properties, compressed "air" would be a "logical" approach. Assuming the cycles of blowing off the dust were kept to reasonable intervals.
The panel performance would still decrease over the same period of time, but perhaps not so drastically.
Martian air would be "free", and the only added weight would be a compressor and storage tank..Again, (wild guess), the only weak in the air supply would be the compressor check valve, A perfect, (or nearly so), seal, would allow air pressure to build up over time, so as not to bleed to much power from the system at once.
Feel free to challenge any, or all, of these assumptions.