What's the minimum time scale for a candle to be lit in order for it to establish a steady state? My Understanding
When a candle is lit initially, it goes through a few stages (see, e.g. this explanation from the National Candle Association):


*

*Wick burns. 

*Crusted wax on wick melts, evaporates and burns. 

*Base of wick warms, nearby wax melts. 

*Capillary action "pulls" melted wax near base of wick up through the wick to where it evaporates and burns.


If I extinguish the candle, then the wax solidifies. 
My Question
Suppose I lit a candle briefly, then extinguished it right away. The wick would burn some of the wax that was in it, but wouldn't have time to pull max up it to replenish the wax that got burned. 
Suppose I did this repeatedly. Eventually the candle wouldn't light as well, right? 
For standard household candles, what's a minimum amount of time to let the  candle burn before extinguishing it so that it replenishes its wax supply and doesn't burn too much of the wick off? A few seconds? A few dozen seconds? A minute or two? How do you know -- that is, how did you estimate this time scale?
If that's too broad, then what factors affect this time scale? 
 A: Factors affect the time (i.e. from start to the time of equilibrium state where the following processes are sustainable: flame heat up wax, liquefied wax being pulled up, evaporated, wax vapor mixes with air, burn and produce heat) are followings,
- size of wick (the larger, the more heat it can produce)
- size of wick (for capillary flow)
- wax type (melting temperature, surface tension etc.)
- environment temperature (hot or cold)
- environment oxygen concentration 
You didn't quantify how much is to too much for burning out wick. So the constraint is not well defined. If we know these, a detailed calculation can be laid out for estimating this time. 
A: I would not immediately know how to start calculating siuch a time, but I can offer some practical observations:

*

*You ask Suppose I did this repeatedly. Eventually the candle wouldn't light as well, right?  The answer is yes, that happens easily (in my experience). The dry wick will then burn completely and cannot be lit anymore (without some digging).


*Even for household candles, the time to stationary (rather: the time until you burn the liquid wax flowing into th wick) probabyl depends on a number of factors (wick, wax, draft, way of lighting,...). However, you can practically assess this state for a given candle by looking for a puddle of molten wax at the base of the candle, togehter with an approximately constant flame.
If there is no puddle, wax cannot have started to flow. If there is one, wax will start to flow and the flame will change in size until the flow rate is reasonably steady, and voilà.
