GE can be weird sometimes. Your letter will Tell you why they denied the increase. I would just request another CLI when the time comes. My Dillard's was one of my fastest growing GE limits, and went from a $700 limit at opening (4/2011) to $7.5k (6/2012). I only use it for maybe one $50-80 purchase every 3 months or so, then PIF.
CC's: AMEX (4), Alliant Visa, PenFed AMEX, Pen Fed Promise, Citi (3), Chase (5), US Bank Cash+, Huntington Voice, Nasa Plat Cash Visa, Barclay's Visa, Discover IT, Cap One QS, BOA (2), BMW Visa, 5/3 Real Life Rewards MC; FNBO Amex; Comenity Visa/MC (3), Ebates Visa Siggy, Nordstrom Visa, Walmart MC, Sam's Club MC; A few assorted store cards.
Current Scores (09/2017): EQ My Fico: 786; TU MyFico: 799; EX (My Fico): 797