。
She kept weaving napkins the whole time.
Literal
She [topic-は] the-whole-time napkin [object-を] kept-weaving.
Two ways of expressing duration stack here: ずっと ('the whole time') as the adverb, and ~続ける ('continue doing') as a verb suffix glued to the verb stem 織り (i-stem of 織る 'to weave'). The pairing is emphatic — ずっと alone or 織り続けた alone would already convey duration; together they hammer it in. 織る is the verb specifically for weaving on a loom — a craft skill that's part of Japanese textile traditions ranging from kimono brocades to traditional ramie weaving in regional villages. ナプキン here is the cloth napkin sense, a Western-style table accessory.