i've a low-cost printer Samsung i provided to configure in my network. i gave it a static IP and connected to my AP. i can ping (and use) the printer only if i'm connected to the same AP. why can't i ping this printer from any other pc in the LAN? the positive thing is that the printer maintained the static IP and every day it's reachable if i'm connected to the same AP. this AP, in order to work, is connected to another AP that is, in turn, connected to the main switch of the workshop.
So, you AP (wireless) is actually a bridge/Extender for another AP, which is connected to the main Switch.
Try looking at the AP Settings to see if certain network segregation is set-up, is the primary AP from your Provider ? because some providers configure their Wireless networks to be split from the LAN network (as is the case with my provider in BE).
Could be as simple as that the AP and LAN are 2 segregated networks.
Can you ping a AP Connected computer from a LAN Attached device ?
What are the ping times when you are not connected to the AP? It doesn't make sense that the AP would be segregated if you are able to ping. If you do an -arp a from a Windows machine after pinging the printer, does the MAC address for the IP of the printer match the MAC of the printer?
If you are able to ping from outside of the AP, and the MAC is correct, I would be curious how you have the printer installed. Is it installed on your machine by IP address?