This work presents an asynchronous multi-robot adaptive sampling strategy through the synthesis of an intermittently connected mobile robot communication network. The objective is to enable a team of robots to adaptively sample and model a nonlinear dynamic spatiotemporal process. By employing an intermittently connected communication network, the team is not required to maintain an all-time connected network enabling them to cover larger areas, especially when the team size is small. The approach first determines the next meeting locations for data exchange and as the robots move towards these predetermined locations, they take measurements along the way. The data is then shared with other team members at the designated meeting locations and a reduced-order-model (ROM) of the process is obtained in a distributed fashion. The ROM is used to estimate field values in areas without sensor measurements, which informs the path planning algorithm when determining a new meeting location for the team. The main contribution of this work is an intermittent communication framework for asynchronous adaptive sampling of dynamic spatiotemporal processes. We demonstrate the framework in simulation and compare different reduced-order models under full, all-time and intermittent connectivity.