As I'm sure you may be aware of, the very best email to use with an Android phone is Gmail. I have five Gmail accounts coming into each of my Android phones and the Captivate and Galaxy SII I have both update quite reliably and fast. I have one Yahoo account which is much slower. I've tried a few others just to see what they are like, yet nothing beats Gmail.
If yours is not updating to your satisfaction I would highly suggest that you check all the settings to be sure nothing got disturbed. I've got a lot of Android phones and the only time I have experienced a delay with Gmail is when I inadvertently changed a default setting when I was initializing the phone. Once I went back in, found it and corrected it, my mail was just as fast and reliable as ever.