Not being ticklish is not a bad thing.
It's a normal variation in how someone experiences touch when not being ticklish and some people are less sensitive or even not sensitive to the tickling than other people are.
A sudden loss of ticklishness can sometimes mean a nerve related issue, but it's not a cause for concern.
Also if you try to tickle yourself your brain won't let you feel the tickling sensation.
The part of the brain that does not allow you to tickle yourself is your cerebellum.
The cerebellum is located at the back of your brain and is the primary brain region which is responsible for preventing you from tickling yourself.
The cerebellum monitors your movements and predicts any sensory consequences of your actions.
And by doing so it cancels out the tickle sensation when you initiate the tickle yourself.
Your brain knows to expect the tickle and so it doesn't allow you to feel the tickle when you've done so yourself.
Basically when you move your own hand to tickle yourself, your cerebellum anticipates the touch of the tickle and the resulting sensation.
The prediction of the tickle allows your brain to suppress the tickle response which makes the tickle sensation less intense or even absence.
Your cerebellum distinguishes between external touch such as when someone else tickles you and the self generated touch is prevented when tickling yourself.
Also the somatosensory cortex that processes touch and other sensory information, is also involved in the tickle response although it's activity is reduced when the cerebellum predicts a touch that is self generated.
The ticklishness is also influenced by factors such as context and mood, with situations of fear or anxiety being able to suppressing the tickle response.