Audio breakup while using Sessionwire can be the result of one of or a combination of a number of issues.
Connectivity to internet via WIFI
Contrary to popular belief, remote collaboration over the internet using Sessionwire does not require high bandwidth. Sessionwire was demonstrated at NAMM using only 3Mbps (0.375MB/s) upload and download speeds for several days without issue! However it is important to note that ethernet was used to connect to the internet.
Stability in the connection to the internet is paramount when working with professional audio software such as Sessionwire - and ethernet is far more stable than WIFI.
Any packet loss over a WIFI connection can result in audible dropouts or glitches in the audio being streamed one or both ways over the peer to peer connection.
You can run a packet loss test in order to determine if packet loss is the main cause or one of the causes of audio break up.
Computer Resource Overload
When working on older computers or on large DAW sessions, audio breakup can result from the host CPU being overtaxed - large plugin counts, complex plugins (IR reverbs, etc) and high track counts can all contribute to CPU overload.
Sessionwire requires resources as well to encode and decode both video and audio - so if the CPU is already taxed by the DAW, adding Sessionwire's processing to that may results in audio breaking up or stuttering on the remote end of the Sessionwire call. Freezing or committing tracks in a heavy DAW session may help smooth out any audio issues that are encountered.