Very long time to update and synchronize mail via WiFi (IMAP).
The problem is only on WiFi, on 3g-4g it updates with good speed.
(Wi-Fi itself also works at a good speed; on a computer via Wi-Fi, mail opens fast, only k9 client is slow.
Maybe different WIFI specifications. Vendors tend to implement WIFI differently. E.g. a Netgear WIFI 5 AP will most definitely not work nicely with Broadcom WIFI 5 chips. Asus APs have trouble with some Lenovo and Dell devices.
Additionally, the encryption mechanism also has an influence on the connection. E.g., Cisco’s WPA 2/3 combo-mode create nasty hiccups with Broadcom chips, but not one from Intel.
So basically, it would be good to know what kind of handheld you are using and with what kind of AP you are connecting.