Here is a review of that psychological research (pdf), and there are more studies linked here (the keyword to look for is "regret"). The paper I linked is:

Gilovich, T., & Medvec, V. H. (1995). The experience of regret: What, when, and why. Psychological Review, 102, 379-395.

This article reviews evidence indicating that there is a temporal pattern to the experience of regret. Actions, or errors of commission, generate more regret in the short term; but inactions, or errors of omission, produce more regret in the long run. The authors contend that this temporal pattern is multiply determined, and present a framework to organize the divergent causal mechanisms that are responsible for it. In particular, this article documents the importance of psychological processes that (a) decrease the pain of regrettable action over time, (b) bolster the pain of regrettable inaction over time, and (c) differentially affect the cognitive availability of these two types of regrets. Both the functional and cultural origins of how people think about regret are discussed.

I haven't seen a study, but that is a common belief. A good quote to that effect,

Regret for the things we did can be tempered by time; it is regret for the things we did not do that is inconsolable. - - Sydney Harris

And I vaguely remember seeing another similar quote from Churchill.