Hello Vlad, and welcome to ESF.
I appears that your blackjack mini is a cartomizer type ecig. Cartomizers are atomizers built in to the cartridge.
Cartomizers are considered in most part to be disposables. (not talking about the battery) 4 days is the typical life of most cartomizers.
Make sure your cartomizers are properly filled. A lot of the prefilled ones are not.
Also are your batteries auto switched or manual? Auto switched batteries are prone to flooding, which can short out the switch. In this case, be careful not to overfill your cartomizers.
You can test these auto switched batteries by holding a DC volt meter on the battery connector while placing the led end in your mouth and giving it a blow, this works in reverse of inhaling to activate the switch. If the switch and battery are still good, you should get a reading of around 3.7 volts on a fully charged battery.
As far as it being clogged, If you can draw on it, then the cartomizer is not clogged.
Cartomizers are only at most a couple of $ each, so cleaning them is just not worth the hassle.
From what I have found on this, that this branded e-cig you have, called the blackjack is a tad overpriced. I would suggest ordering from a reputable supplier with much better prices. Not to worry though, as it has been said many times before, just chalk it up to a learning expense.