I am reading Bearss’ History of the Vicksburg Campaign. I’m on the first volume, and General Hamilton is playing a big part, yet soon thereafter I don’t recall him being present during the rest of the campaign.
I looked up his records, and he apparently resigned his post in Mid April 1863. The summary I found said he was critical of Grant and his superiors, the Wiki gives no reasons. Certainly at that point Grant was down the river, with Corps commanders McClernand, Sherman, and McPherson. If Hamilton was still in North Mississippi, a backwater, could have rankled. Also the elevation of McPherson and/or McClernand could well have rankled.
I’ll have to see if the subject is mentioned in the book when I get to it. It may not be that big a thing – this was a period where many of the larger players in the early war were moving aside or being pushed aside for younger officers. For example in the east, Franklin, Sigel, Sumner, Franklin are being phased out in favor of Hancock, Reynolds, Sedgewick, and Meade.