If antibodies are not detected 6 months after moderna vaccine is there still protection?

Which antibodies ? The vaccine creates antibodies specific to the vaccine which also protect against Covid, not the antibodies tested to detect past wild Covid disease. You should not expect the vaccines to turn that test positive. While tests for vaccine antibodies are available they are seldom use outside research centers.

If you took both doses of the vaccine, you are protected from Covid-19 illness and hospitalization. Testing for antibodies is not recommended. Very few laboratories can perform the gold standard viral neutralization test. Wish you good health!

Yes, you could be still be protective with memory B and T cells which are created by vaccination.