Is the list of words with a contracted "not" closed?

As a rule of thumb, not only contracts with auxiliary verbs. There may be some exceptions. For example, it could be argued that in I haven't the time or the energy the verb HAVE is not an auxiliary. But note that this verb can used as an auxiliary. So we could probably reformulate that as only verbs that are sometimes auxiliaries can contract with not.

The auxiliary verbs in English are BE, HAVE, DO and the modal auxiliaries, the central members of which are:

• CAN, COULD, SHALL, SHOULD, WILL, WOULD, MAY, MIGHT and MUST

There are also a few so-called marginal auxiliaries:

• DARE, NEED, OUGHT, USED

I may have missed one or two marginal auxiliaries there.

In short, the verbs that can contract with not in English are best thought of as a small closed class. Although there is always some change on the periphery of the class (consider USED for example), the English auxiliaries are generally considered to be a closed class.