You should be able to suspend or hibernate each system without it affecting the wireless connection of the other.
I would first recommend resetting the router/access point. To do this, unplug power from the unit and if it has an internal battery then remove the battery for a minute or so. Then reinstall the battery and reconnect the power.
I also recommend installing the latest drivers for the wireless network adapters in your system. If they are Intel adapters you can get the latest driver here
Finally, another very common issue causing wireless disconnection problems stems from power management. Frequent disconnections can often occur when the adapter is configured for aggressive power savings (especially when on battery power). I recommend changing the power management settings for the wireless network adapter
to "Maximum Performance" (or minimum power savings) for both AC and battery operation. This may reduce battery life slightly but I'll happily trade that for a stable connection.
Let me know if any of this corrects the problem. Scott.