How can I make my Apple Watch more sensitive to falls?

There are no settings I am aware of that will affect the sensitivity of fall detection in an Apple Watch. To my knowledge that system does not get "trained" in any way as the Watch gets used. For information, see:

Use Fall Detection with Apple Watch - Apple Support

You can try turning Fall Detection off and back on again and see if that helps.

Apple is trying to strike a very difficult balance between detecting actual falls and incorrectly going off for occurrences and activities that are not really falls. As an example, there were multiple stories a couple of years of people having fall detection triggered while skiing and reports of ski patrols complaining about these erroneous emergency calls, so Apple may have tried to tighten up on these false triggers. My experience is that that most true falls are detected, but that's not always the case, and to my knowledge there's nothing we users can do about it.

Regards.

There is no evidence that responding "I didn't fall" will reduce sensitivity.