There seems to be something odd with the requester chest, but I'm having trouble reproducing it reliably. At certain times it seems to get "stuck" and won't fulfill any further requests.

I've played around with different arrangements (unavailable/unresearched items in the list, gaps in the list, etc.), but can't figure out what the trigger is.

Image of a "stuck" requester chest (check the right-hand overlay to see that some of the requested items are, in fact, available):
https://i.imgur.com/UPq3oJo.png

One common way that seems to cause sticking is if I have two groups of items on two lines. The chest never seems to "see" the item(s) on the second line.

https://i.imgur.com/R5td3Nj.png

to fix your issue a rescan could help. see map setttings.

BTW The Logistics Center uses a Lua scripted logic to implement the chest-logistic system. which is slow compared to build-in systems.
For this reason, I will not invest much more time in this mod.
Have a look to my Smart Linked Chests mod. that solves the chest logistic problem much more .efficiently.

Hmm, I suppose. I do have Smart Linked Chests installed, but liked the early-game aspect of this one, as well as the way it's more strictly focused on logistics.

(For what it's worth, I did notice that it seems to stop reading after the first 5 slots.)

Feel free to close this then. 👍

the early-game aspect is implemented by default also in Smart Linked Chests. see global settings,
https://prnt.sc/9CZnh6S8STxy

Smart Linked Chests and Logistic Center are doing the same thing, with both you can use chests to move items from a to b quickly. ;-) with Smart Linked Chests you can not store a large amount of items in the chest itself, but that can be compensated with warehouses.
https://prnt.sc/Q7QdrwVaR6Tr