In order to develop a long-lifetime MCP-PMT under high rates of circumstance, we investigated the degradation of the quantum efficiency (QE) of PMT's with a multialkali photocathode. We found that not only positive ions, but also neutral residual gases would damage the photocathode resulting in an enhancement of the work function: their countermeasures were established in newly manufactured square-shaped MCP-PMT's with 4 or 4 x 4 multi-anodes. The performances of the PMT's were measured: QE was stable up to an integrated amount of anode output charge of 2-3 C/cm(2), while keeping other basic performances steady, such as the time resolution for single photons (sigma(TTS)) of similar or equal to 40 ps, a photoelectron collection efficiency (CE) of 60%, a multiplication gain (G) of a few x 10(6), and dark counts of 20-300 Hz. The causes of QE degradation are discussed. (C) 2010 Elsevier B.V. All rights reserved.