Why would a deletion mutation in the DNA base sequence lead to the production of a non-functional enzyme?

Because the deletion mutation would cause a frame shift in the DNA base sequence and hence would lead to the formation of new base triplets. As a result, the primary structure of the enzyme would be different and hence hydrogen bonds would be formed between molecules at different positions on the amino acid chain. Therefore, the primary structure would fold differently to produce a differently shaped secondary structure and consequently a differently shaped tertiary structure- the enzymes active site. This newly formed active site wouldn’t be complementary to the substrate that fit into the enzymes original active site and hence the enzyme produced would be non-functional.