How often you should get your horse clipper blades sharpened will very much depend on the clipping you are doing.
The thickness of the coat, length and whether it is clean or not will have an effect on your clipper blades. If you are cutting through a greasy coat you will find that they become blunt much quicker.
In order to preserve your clipper blades and keep them sharp as long as possible it is important to take good care of them. Make sure you are using the correct blade type for the job, for example a hairy cob with a thick coat may need a coarse blade whereas a fine thoroughbred may only need a fine blade. Clipping legs and hogging manes should in general be done with a medium or coarse blade.
Make sure that you keep the blades oiled regularly; Lister recommend re-oiling after every 10 minutes of clipping time. Make sure you use the correct oil type for your clippers. Bottled oil rather than spray is recommended as the spray types can be thinned down and so will not be the right consistency for the blades.
Make sure you have the tension set correctly, what might be the correct tension for Lister clippers may not be correct for Liveryman for example or other brands. To avoid the blades from getting hot you should ensure that the tension is at the minimum possible while still clipping correctly.
Wherever possible ensure that the horse is prepped well to be clipped. Ideally you will have bathed their coat so that the grease is removed, at least a good grooming to remove as much grease and dirt as possible as a minimum. If bathing is not possible then it might be worth taking the majority of the hair off with coarse blades first then re-clipping over with fine blades if this is the finish that is preferred.
You will notice that your clipper blades need sharpening as it will become more difficult to cut through the hair. You may also find that they start to leave lines in the coat or do not cut as close as usual. Depending on the clipping being done you may find that blades need sharpening between 4 and 10 clips.
It is important to keep your blades sharp as not only will this make life easier when clipping but will prevent any tugging at the hair which will irritate and could upset the horse.