Some folks may play 10, 15 minutes every second day.  Some can put in anything between 2 and 8 hours per day - so - the "smart answer" is as and when needed.  

But how do you determine that ?

Well, I can only speak for myself - ( and I play up to 2 hrs per day in 20 or 30 minute slots ).  With the bow I have ( a FiddlerMan CF bow ) and the rosin ( Kaplan Dark ) and the strings I use, and the "type" of practice I'm doing (slow gentle pieces, or hard, fast, and furious - which can shed rosin more easily off the hair ) I find the following two indicators - 

(1) I'll maybe notice a tendency for the E string - especially if it is a plain steel string I have fitted at the time to "squeak" or "squeal"

(2) Much more noticeable however for me is a very definite tendency for the hair not to grab on the G string, and start to "glide" over it rather than grab it.  

Now, I have, over time, just "fallen into" identifying the "onset" of these conditions, and generally become aware of it starting to happen before it really sets-in - and I'll re-rosin.  So, largely because of my different playing styles ( pp or hammering the strings to within an inch of their life ) - I cannot possibly give any sort of accurate "time between rosining" - if I HAD to, I *guess* it feels like after around 5 to 10 playing hours (again, with the bow, the rosin, the string types and bowing pressure all being part of the equation).  And when I do re-rosin, my own application technique (for the bow and rosin I use) is typically 5 full, both way strokes across the rosin cake, with an "intermediate pressure" ( not too light, and not so hard it pushes the hair to the stick )

There MAY just be another point worth making - I understand it is possible to "over-rosin" the bow to the point where no more can adhere - is it possible that's what's been happening - because you say "On the surface of the rosin it forms small white beads." .... just wondering....   Also, if that were the case, your strings (unless you clean them as well - a rag, or the old wine-cork with a slit in it trick ) my well be caked with rosin at the sounding point, making it even more difficult for the hair to grab....

Just some idle thoughts from my own perspective....  it can be all very much about personal choice of materials ( bow, hair, strings, rosin, bowing sped, pressure, angle and so on ) and FAR too subjective to give any one definitive answer - good luck !

Interesting, @cdennyb - it (rosining when you need to) is a "finely judged thing" - and you just "get to feel/understand" it, in combination with your normal playing schedule, I get that, and indeed, at the end of the day - we're all different - and "feel" it differently, absolutely - there is no written rule about this !

I would also guess, that if you or I played/practiced the 8 or 10 hours-plus Garrett (allegedly) does or did per day - he would just stop - at a guess - every couple of hours, and do a quick re-rosin - but who knows the secrets of the gods-themselves - I ask you - who knows ????  LOL

But the whole "violin thing" for me, is a truly interesting symbiotic relationship between man and instrument ( well, between the player and the natural physics of all the items involved in playing - from micro-control of shoulder, arm and wrist muscles, to finger-control of the bow, its speed, angle and pressure, the bow hair, rosin type, bow angle and so on...

That's not to mention the strings, their specific tuning ( like a semitone lower - 415 instead of 440 on the open A ( well, no longer an "A" but you know what I mean ) which seems not to be wholly uncommon - and other aspects affecting tone production whilst playing - LISTEN TO ME - like I KNOW something...  no, not really - but I do have an "insight" into what's happening whilst playing, and "why things sound like they do" ( or not, as the case may be )

There are a huge number of effects that affect the sound production - some folks - like "engineers, rooted in the physical sciences" can kind-of-understand - if not in actual detail - what's going on, some folks who know NOTHING about the "physics" of the thing just "get it" automatically without even having to THINK about it (jeez, lucky folks) , and some folks just have to "work with it until it becomes automatic" - each and every approach is fine - it all takes time - whichever way you come to the violin....  basically, never give up is what I say.....   

Live your dream !

COOL !   I was kind of wondering about that ( excess rosin ) - but clearly you also have a separate issue there climate-wise and although I have never experienced it, I can believe it. 

Great news !

With YOUR rosin of-your-choice, YOUR local climatic conditions, YOUR playing hours, YOUR playing style (speed, pressure,angle etc),  I have no doubt you will now "start to be aware" of just when the bow-hair is whispering to you "rosin-me, rosin-me....   NOW"  - you have to listen VERY closely !!!!   LOL

So glad you've got a "handle-on-it"