Well system pressure drops suddenly
We have a deep-well (230 feet) domestic water system. I usually turn off the pump and electric water heater when we'll be away for a while, partly to save electricity and to limit damage in case a pipe bursts. When we returned home after being away for a few days, the whole-house filter filled with sediment, but the system pressurized. I turned it off again and replaced the filter. It promptly filled again. I decided that now was the time to replace the 28-year-old pressure tank and add a sediment filter in the line before the well water gets to the tank. All went well and the system functioned fine until the first drawdown of the tank. When the pressure decreased to the cut-in point for the pressure switch, the pressure dropped to almost nothing and stayed that way for about 30 seconds. Eventually pressure returned and the system pressurized normally. But it keeps doing this every time the pump turns on. I've tried adjusting the pressure on the bladder tank to no avail. Is there a pump problem? I hate the thought of pulling that out of the ground unless I have to.