one. If you're losing 3 in a row, you're doing something wrong. Either your hook is dull or your hook-sets are crap. Can happen if you have too much loop in your line to your float or if you're using mono and let your drift go very long.
I agree that the hook sets are undoubtedly crap (or else you would not lose the fish), but I disagree that you must be doing something wrong. The hook set (where in the mouth you hook the fish and how well you do so) is a combination of the timing of the set, the position of the fish in relation to you, the direction it moves after taking the hook, how quickly it tries to spit it out, etc. With so many variables affecting the quality of the set (including, yes, the sharpness of your hook), not to mention all of the possible scenarios that could cause a well set hook to come loose (ie: snags), the possibility of going 0-3 is entirely possible even if you are doing everything right. If you have never lost 3 fish in a row before landing one then you are a great and lucky fisherman indeed (or you are using barbed hooks).
I personally had a rough stretch last season where I had a few in a row come loose after a brief head shake or longer (I was not counting but it had to be 4 or 5). I have not had the chance to even loose one so far as I have not even had a sniff so far in a half dozen trips on the fly.