Body Sensor Network (BSN) is a typical Internet-of-Things (IoT) application for personalized health care. It consists of economically powered, wireless and implanted medical monitoring sensor nodes, which are designed to continually collect the medical information of the target patients. Multichannel is often used in BSNs to reduce the spectrum competition of the tremendous sensor nodes and the problem of channel assignment has attracted much research attention. The health sensing data in BSNs is often required to be delivered to a sink node (or server) before a certain deadline for real time monitoring or health emergency alarm. Therefore, deadline is of significant importance for multichannel allocation and scheduling. The existing works, though designed to meet the deadline, often overlook the impact of the unreliable wireless links. As a result, the health sensing data can still be overdue because of the scheduled lossy links. Besides, potential collisions in the schedules also incur considerable delay in delivering the sensing data. In this paper, we propose a novel deadline-driven Link quality Aware Channel Assignment scheme (LACA), where link quality, deadlines and collisions are jointly considered. LACA prioritizes links with urgent deadlines and heavy collisions. Besides, LACA allows the exploitation of the spare slots for retransmissions on lossy links, which can further reduce the retransmission delay. Extensive simulation experiments show that compared to the existing approaches, LACA can better utilize the wireless spectrum and achieve higher packet delivery ratio before the deadline.