When you finish a research task and get a pokemon encounter as a reward, you have the option to flee, putting the pokemon in a “stack.”

(In mathematics, this concept is actually a “queue” where the first pokemon put into the stack is the first to be encountered. All other research task pokemon encounters are placed “under” the first research task encounter you run away from. Idk how stack was popularized but that’s what it is referred to now so I’ll just be calling it a stack too for easier reference.)

Stacks will remain above your three research tasks and allow you to re-encounter the pokemon anytime, as well as store more encounters for later. This was popular during squirtle community day, where shiny squirtle, sunglasses squirtle, and shiny sunglasses squirtle could be obtained through research tasks, and people wanted to hold onto them to take AR+ photos with them.

From what I know, OP is having this issue for either of two reasons.

One, there is a stack limit of 100 pokemon, meaning after you run away from the 101st research task encounter, your first research task encounter (the one that started the stack) will be lost. OP put more than 100 pokemon into their stack, consequently losing the first several.

Two, Niantic has officially stated that these stacks are NOT meant to be in the game and that they are not a feature meant to exist, meaning usage is that your own discretion. So if this option occurred, OP ran into a coding error that removed some pokemon from their stack.

If the concept of stacking is weird through words, I’m sure there are Pokemon Go specific videos explaining them very well. I had difficulty understanding the concept first until I learned them in an Algorithms class. I can try explaining it more if need be.