Some of these older machines have what's called a lint filter on them. Not sure about the Maytag. That's about the only thing I can think of that may hold water long enough to get stagnet. It's mounted on the outside of the tub and has a small port that connects it to the tub. If yours has a filter it can be seen by lifting the top and looking down. There should be two hoses attached to it.
I've always felt like they were kind of a sales gimmick. There's no "replacement" filter unless you go to the trouble of replacing the whole thing. The theory is that when the water is pumped out it passes through the filter and washes any lint away. Any small amount of leftover water will collect at the bottom of the filter.
The bleach thing sounds like a good idea, but you'll need to fill high enough so it enough so that it enters the filter through the port. I'm not sure 1/4 full would be enough. My top loader looks like it would need to be at least half full to reach the port.
Hope this helps.
Edit: Was just looking at Maytag parts. Your machine may have a lint filter, but is different than the one I described on my Whirlpool. This is the Maytag filter. http://salestores.com/maytag01.html Not sure where it would be located on the Maytag, but could still be the source of the problem. My Whirlpool filter looks like this. http://www.appliancepartspros.com/Ap...AP2913852.aspx
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