One of the more surprising things (to me, anyway) that I’ve learned about GFP photobleaching in live cells is that it is strongly dependent on redox environment. It has been shown that GFP can undergo photochemical oxidation to a bleached form and then to a red form . The electron acceptors in this oxidation can be various cellular components including flavins and flavoproteins and NAD+. This appears to be a major cause of GFP bleaching in vivo. It can be greatly reduced by removing riboflavin or all vitamins from the culture medium DMEM . More recent work showed that GFP bleaching due to riboflavin in the culture medium can be suppressed by adding rutin, a plant flavonol, 30 minutes prior to imaging .
If you’re concerned about GFP bleaching in your cells, it’s worth trying DMEM lacking all vitamins. It’s commercially available from Evrogen as DMEMgfp. It probably has lower fluorescent background as well. Rutin is commercially available as well, and easy to try if you don’t want to use DMEM without vitamins. There is a report in the literature that Trolox can reduce the bleaching of EBFP  but it is not clear if this is true for EGFP as well.
As an aside, the GFP oxidative reddening can be used for photoswitchable single molecule super-resolution imaging as well .
A.M. Bogdanov, E.A. Bogdanova, D.M. Chudakov, T.V. Gorodnicheva, S. Lukyanov, and K.A. Lukyanov, "Cell culture medium affects GFP photostability: a solution", Nature Methods, vol. 6, pp. 859-860, 2009. http://dx.doi.org/10.1038/nmeth1209-859
A.M. Bogdanov, E.I. Kudryavtseva, and K.A. Lukyanov, "Anti-Fading Media for Live Cell GFP Imaging", PLoS ONE, vol. 7, pp. e53004, 2012. http://dx.doi.org/10.1371/journal.pone.0053004
A. Matsuda, L. Shao, J. Boulanger, C. Kervrann, P.M. Carlton, P. Kner, D. Agard, and J.W. Sedat, "Condensed Mitotic Chromosome Structure at Nanometer Resolution Using PALM and EGFP- Histones", PLoS ONE, vol. 5, pp. e12768, 2010. http://dx.doi.org/10.1371/journal.pone.0012768