Is it possible to lose Insight?

Solution 1:

You don't ever lose it from dying, some enemies steal it. A couple areas are harder if you have 15 or more. It's pretty easy to get if you just want to spend it though.

Solution 2:

There is an enemy in the area below the Cathedral, which becomes accessible after the Blood-Starved Beast boss, that is very reminiscent of the guards in Latria's Tower in Demon's Souls. It has a paralyzing attack and then sucks two insight out of you per attack.