My experience is that you can have many connections from the same source IP without the ASA disconnecting you. However, the base SSL VPN license on an ASA allows only 2 SSL VPN connections. If you were hitting that limit I would expect you to get a credential failure, not a disconnect.
Is there a possibility that multiple SSL VPN connections are being initiated from the same machine (ie. Terminal Services), or someone is logging into a box through RDP or TS that has an already established SSL VPN connection? Default behavior for AnyConnect is to disconnect the VPN if this is the case.
James