Any VPN client, not just the Cisco AnyConnect one, can and will drop the connection if it is of poor quality. Although there may be ways to "tweak" the client to be less "sensitive," I would suggest that you work on improving the Wi-Fi connection between your MacBook Air (MBA) and the wireless router.
One measure of wireless signal "quality" is the Signal-to-Noise Ratio (SNR). SNR = RSSI - Noise. You can determine this with your MBA, by looking up both RSSI and Noise from the Wi-Fi dropdown menu.
To do so, hold down the <Option> key, and then, click on the Wi-Fi icon on the macOS menu bar. You should find both of these values and a few others that will represent the current connection state between your notebook and the wireless router.
You can use the following to compare against what you find:
SNR Guidelines
- 40+dB = Excellent signal
- 25dB to 40dB = Very good signal
- 30dB = Minimum range boundary (voice)
- 15dB to 25dB = Low signal
- 20dB = Minimum range boundary (data)
- 10dB to 15dB = Very low signal
- 5dB to 10dB = Little or no signal
Using the above guidelines, you will want your MBA connected at, at least, 25dB or higher. This should keep the VPN client "happy."