How long does it take for dopamine to reach normal levels after a significant drop?
I can see a couple of problems in the question:

First problem, you assume that anergia (not sure that's how you call being tired) after sex is caused by dopamine depletion, I'm not sure this is the case or that lack of dopamine has been related to anergia at all. We know from Parkinson patients that Dopamine is related with action initiation (http://www.nature.com/nature/journal/v466/n7305/abs/nature09263.html) not necessarily with lack of energy or motivation. 

Second problem, depletion (the term you originally used) means no more dopamine is system, either because you block it somehow (antagonist), you block its receptors (receptor antagonist) or you block one of the precusors involved in synthesizing it eventually depleting your reserves. "Significant drop" needs to be quantified.

Dopamine (DA) synthesis is an ongoing process, and DA is an essential neurotransmitter / neuromodulator in the brain just like Serotonin (more on that later). This means that it probably has different roles. One phasic referring to its neurotransmitter properties and one tonic referring to its global levels in the brain and how it modulates ongoing synaptic activity.

Normal activity does not deplete DA, and yes, no matter how crazy you think you are, sex is considered normal activity. You can obviously have variations of basal levels of DA depending on your activity but they are way removed from the depletion criteria.

Furthermore, the brain is very parsimonious in its synthesis efforts, it has specialized molecules that recover neurotransmitters that where unused from the synaptic cleft, these molecules are appropriately called reuptakers.

Now to attempt to answer your question considering the problems:

I don't know about DA but I do have some experience with serotonin depletion.
Serotonin (5-hydroxytryptamine, 5-HT) is synthesized from tryptophan that you cannot produce endogenously. Lucky for us that tryptophan is in almost every food we eat which means that there is no lack of it.

You can, in experimental conditions, ask people to drink a glass of a very disgusting liquid that will bind to your tryptophan preventing it from being used in new 5-HT synthesis. It takes approximately 4-6 hours for it to work (e.g. http://web.stanford.edu/~knutson/ans/bjork99.pdf methods section), which means that in 5 hours you used up all your reserves of 5-HT. This meansthat your "refilling" process would be about the same time  in order to get to pre-depletion levels (you might be able to be in a functional regime before that if you ignore the reserves part).

So from this 5-HT example I would say that unless something is very different in the case of DA to recover from depletion it would have to be in the hours time frame.

Another way of looking at it can be looking at the half-life of the molecule which gives you an idea of how much time it lives. This can be used to calculate how much production there has to be to maintain a level of X. The turnover is the amount of time that it takes to, well, turn over, so replace DA in the system that should be in the same order of magnitude as coming back from a depletion experiment.