Timeouts that long and lost packets suggest your AP (or possibly your wireless client) might not be doing a good job of supporting 802.11 power save mode. When a client uses power save mode, the AP is supposed to queue up packets for that client, and notify the client of the waiting traffic in the next beacon, and in all further beacons until the client requests the queued packets in one way or another, or until the AP gives up or needs the packet buffers back.
The typical rate for beacons is one every 102.4ms, so even if the client is in power save mode, it should get the queued ping request in 51ms on average, 102.4ms max, and reply within 1ms, so I wouldn't expect power save mode to cause pings much longer than 104ms.
Then again, a client can choose a "listen interval" which is a number of how many beacon intervals it wants to keep its receiver shut off for. If the client was choosing a listen interval of 10, it would only be waking up once per second (assuming a typical 102.4ms beacon interval from the AP), so you could see 513ms average, 1025ms max pings in that degenerate case. But I'm pretty sure Macs never trade that much latency to get a little extra power savings. That's something you might see from a low-throughput Wi-Fi device designed to run a long time on a tiny battery.
If any of Synergy's traffic is multicast or broadcast, there's a separate "DTIM interval" for how often the AP will send out multicasts/broadcasts to all clients.
What is the make, model, hardware revision, and firmware-version of your Wi-Fi AP? Is your firmware up to date? If your AP lets you set your Beacon Interval or DTIM Interval, how do you have those things set?
An 802.11 monitor-mode packet capture of the problem happening might be useful. Macs make this reasonably easy to do via the semi-hidden Wi-Fi Diagnostics tool, but you'd have to have a second Mac to do it from because the device having the Wi-Fi problem is never a trustworthy impartial observer.