A quick review of recent literature:
Reputation does appear to affect alliance behavior. A strong reputation for sticking with past alliances affects alliance formation and dispute resolution. (1)
Crisis behavior is less clear. Failed (or successful) crisis deterrence, for example, doesn’t seem to matter as much as is commonly assumed in the literature in strategic signaling. In fact, the effect of past action (standing firm, or backing down) on reputation seems to be pretty low. (2)
Some of the most interesting work is being done of the expected domestic consequences of backing down, and what effects that has on foreign policy. In democracies, regardless of whether or not reputation has a strong effect on foreign leaders, the belief by key domestic audiences that it does, and the expectation by a democratic leader that he would suffer politically if he were seen to back down, does seem to lead to a stiffening of the spine by that leader. (Consider JFK’s comment on Cuba, that if he let the provocation slide he’d be impeached.) (3)
When it comes to deterrence (of various kinds), there have been few studies of the effect of reputation. Those that have been done find “little support for the strong-interdependence-of-commitment argument that potential attackers infer the defender’s reputation for resolve from its prior behavior in disputes with other states across a broad range of geographic locations.” (4) It’s not that reputation is insignificant, but its significance is very context-dependent, and situational variables are consistently more important. It also appears that “lessons learned” don’t stick for very long, as the strategic situation changes and/or leaders are replaced. The middle east--especially the Arab-Israeli dispute--is a good example of this.
(1) Gibler, Thomas M. The Costs of Reneging: Reputation and Alliance Formation. Journal of Conflict Resolution; Jun2008, Vol. 52 Issue 3, p426-454.
(2) Danilovic, Vesna, and Joe Clare. Reputational Effects of International Conflicts. Conference Papers — International Studies Association; 2007 Annual Meeting.
(3) Tomz, Michael. Domestic Audience Costs in International Relations: An Experimental Approach. International Organization; Fall2007, Vol. 61 Issue 4, p821-840.
(4) Huth, Paul K. Deterrence and International Conflict: Empirical Findings and Theoretical Debates. Annu. Rev. Polit. Sci. 1999. 2:2548. Huth is probably the leading researcher in this area. He's certainly one of the best.