Actually it's very like going to the gym.
You going in as powerful as you can, you doing weight lifting and other exercises and when you leaving the gym, your legs and arms are like jelly at the beginning. You are weaker than you went in. Your muscles are hurt, you don't have too much energy at all. But with more practice you getting stronger and stronger.
It can be less dramatic if you doing it with "thinking", but can be very painful if you "overdoing" it.
Snape wasn't really kind, that's true. He wanted to train Harry on "full speed" from the first second... it's like trying to lift 100 KG on your first day in the gym. He is not a good coach because of his feelings about Harry (he hates him yet is protecting him) - he simply does not have the patience required for this training.
The last thing he wants to do is to hurt Harry, though - there are several occurrences/cases in the series where Snape protects him.
He is just not the right person for the job - yet he is the best person for the job as he proves he can hide things from Voldemort.
I'd say the temporary weakness is the nature of the training but the small success is because of Harry himself (he resists and wants to use the connection to look into Lord Voldemort's mind) and Snape's lack of patience.