Hello. 

I have the exact same problem as described in https://community.tp-link.com/en/home/forum/topic/673210

The management interface becomes unavailable from a trunked port after approximately 4-5 mins. If the switches IP is pinged from the L3, the UI becomes available again. 

It is not from the arp expiry at the L3 (i'm using a pfsense) 

Connecting locally at the TL-SG1428PE, you can navigate to the webui without issue. It's ONLY when the UI is accessed via a trunk. 

To replicate.. 

Switch - Vlan and trunk port to Firewall

Firewall - 2 vlans - one VLAN with the switch subnet / IP, another Vlan for a laptop. Allow access through firewall rules. 

Attempt to access web UI IP address - it will fail after approximately 5mins. 

The only way it can be restored is to connect to the switch locally / vlan. OR ping from the firewall / L3, this seems to wake the UI up. 

Gateway etc all set correctly.