Your explanation is a bit confusing, although correct. I believe this person here [1] explains it better, with more examples. The key is to “stop thinking” of these two structures as similar to each other: They're not.
[1] https://www.quora.com/What-is-the-difference-between-stop-do...
1. Let's ensure wise men don't stop to share their wisdom
2. Let's ensure wise men don't stop sharing their wisdom
If you say, "don't stop to do X," that means (roughly), "don't do X." In other words, #1 means the same thing as, "Let's ensure wise men don't share their wisdom." #2 is the one you want. If the amount of multiple negatives is confusing, omit them completely and say, "Let's ensure wise men keep sharing their wisdom."