So, she was pretty attached to it. The spout on this cup is made of the same material as a bottle nipple, so of course, with time, and use, it started to get weak. Me boiling it every other day probably contributed to this quite a bit. Anyway though, long story short, we had to get a new cup.
Trying to be savvy, I bought a different style cup, a more “grown-up” cup, that was made of a different material. I figured it would take longer to wear out, plus it would help her to learn to use a “regular” sippy cup. This: