Q: iTunes, Remote and Apple TV synching problems.

Is the computer a Windows system?

If so, perhaps try checking for a LSP issue as per the following document:

Apple software on Windows: May see performance issues and blank iTunes Store

(In theory a LSP issue would be consistent will all your symptoms, although I'd expect the trouble to be persistent rather than intermittent.)

I had the Same issue.

Narrowed down to my Netgear ProSAFE Plus 16 Port Gigabit Switches

Using the Configuration utility, I turned OFF Multicast – IGMP Snooping Status.

Why I do not know, but this one change made everything work.

Validated by turning it back on and the Itunes / Iphone issues returned.

Is Apple Home Sharing using IGMP?

IGMP snooping is the process of listening to Internet Group Management Protocol (IGMP) network traffic. The feature allows a network switch to listen in on the IGMP conversation between hosts and routers. By listening to these conversations the switch maintains a map of which links need which IP multicast streams. Multicasts may be filtered from the links which do not need them and thus controls which ports receive specific multicast traffic.

A switch will, by default, flood multicast traffic to all the ports in a broadcast domain (or the VLAN equivalent). Multicast can cause unnecessary load on host devices by requiring them to process packets they have not solicited. When purposefully exploited, this can form the basis of a denial-of-service attack. IGMP snooping is designed to prevent hosts on a local network from receiving traffic for a multicast group they have not explicitly joined. It provides switches with a mechanism to prune multicast traffic from links that do not contain a multicast listener (an IGMP client).

IGMP snooping allows a switch to only forward multicast traffic to the links that have solicited them. Essentially, IGMP snooping is a layer 2 optimization for the layer 3 IGMP. IGMP snooping takes place internally on switches and is not a protocol feature. Snooping is therefore especially useful for bandwidth-intensive IP multicast applications such as IPTV.

I'm using a TP-Link Archer C3150.

I found that with the "AP Isolation" feature turned on i was unable to "see" the Apple TV using the Remote app.

As soon as this setting was disabled, I was able to connect to the Apple TV with no problem.