Weekly / Daily
Daily I check if all GPUs are still working (via teamviewer or similar software). I notice often that on some of my rigs one of GPUs stops working. I see it in device manager, but Afterburner and miner just ignore it. After restart everything is back to normal.
Weekly I check temperatures and fans. If fans are spining and temperatures are in the safe zone and your enviroment isn't extra dusty then there is nothing to worry about.
Monthly
No special maintence / same as weekly...
Yearly
While GPUs are in warranty I will only clean dust every 6 months or before if necessary. When GPUs go out of warranty (and if I don't sell them before that) I will remove fans, clean them thoroughly and replace thermal paste.
This is similar to my maintenance plan. If everything is working correctly (i.e. the rig is stable and temperatures are ok) there is no need to go in and mess with your hardware as you have a greater chance of screwing something up yourself. Physical dust build-up, while unsightly doesn't necessarily affect cooling as much as you would think by visually looking at it.
All these components we use are designed to go into a computer case, which often times will not get opened up for over a year. I have seen normal PCs (not mining rigs) that have had a year plus of dirt, hairballs, dust-bunnies, etc., build up inside and when it does get opened, say to upgrade a graphics card you wonder how it even ran. The point is manufacturers know these components will be used in dusty conditions so they are built to some degree to survive in this. I actually think open air frame shave an advantage here as even though they may look dirtier since there is no enclosed case to hold in heat the ventilation (even dirty) is far superior.
With all that said, there comes a time when a simple cleaning is required, but I would say this should be performed no more than once or twice a year.