Several studies have suggested that negative memories fade faster than positive memories: Walker, Vogl and Thompson (1997) had the subjects kept dairy during a 3-month period, and rated the events on a pleasantness scale each time, memory tests were conducted on various intervals: 3 months, 1 year and 4.5 years. Results showed that pleasant events are remembered better compared to unpleasant ones, unpleasant ratings also decreased more than pleasant ratings compared to the original ratings. Ritchie et al.(2009) found that the fading affect for negative events is greater than its fixed affect. Kensinger (2008) found that older adults remembered positive nonarousing words better than negative nonarousing words;
There is Taylor's (1991) mobilization-minimization hypothesis trying to explain this phenomenon, are you aware of any studies addressing this phenomenon with neural data?
Kensinger, E. A. (2008). Age differences in memory for arousing and nonarousing emotional words. Journals of Gerontology: Series B: Psychological Sciences and Social Sciences, 63, P13–P18.
Ritchie, Timothy; Skowronski, John J.; Hartnett, Jessica; Wells, Brett; Walker, W. Richard (April 2009). "The fading affect bias in the context of emotion activation level, mood, and personal theories of emotion change" (PDF). Memory. 17 (4): 428–444. doi:10.1080/09658210902791665.
Taylor, S. E. (1991). Asymmetrical effects of positive and negative events: the mobilization-minimization hypothesis. Psychological bulletin, 110(1), 67.
Walker, W. R., Vogl, R. J., & Thompson, C. P. (1997). Autobiographical memory: Unpleasantness fades faster than pleasantness over time. Applied Cognitive Psychology, 11(5), 399-413.