This is an explanation from my department chair which I've expanded. In the context of a university, there are four main power groups - the alumni, the faculty, the students, and the board of trustees. (Within each group of course are subfactions.) The actual power balance between these groups is never precisely certain (it's an unobservable "latent variable"). Whenever large events happen that involve the university, we get observations that allow us to estimate the latent variable better.
In the case of Harvard, I think the current observations are most consistent with the following: the Board of Trustees, faculty, and students have currently aligned in their goals - which we might summarize as (1) maintaining independence from the government and (2) the ability to hold/teach specific "controversial" viewpoints (benefits of diversity, anti-colonialism, potentially other "progressive" concepts). I suspect that within the factions the relative importance of these two goals is not balanced. The fact that the coalition has survived much longer than, e.g., Columbia, is somewhat surprising.
My suspicion is that the answer to your question is that the persistent "smacking around" is only in part due to the external factors other replies have mentioned. I think a major piece of the situation can be explained by a change in the power dynamic with the alumni. Under normal circumstances, the faculty presumably hope to maintain long lasting influence over their alumni, which the board of trustees leverage to bring in more money and influence to the university. The current situation suggests that the high-power/high-$$$ portion of the alumni who are in a position to leverage the public conversation about what's going on are not doing it. This implies that the strength of that edge of the power graph is much weaker than it was expected to be. I think it remains to be seen whether this is true. Further observations that would support that would be reduced donations, public complaints, etc. Conversely, increased fundraising and more public support would suggest the opposite.
The key point about the university power network is that USUALLY, the best situation is to avoid situations that actually reveal too much information. Everyone would prefer to believe they have more power than they do. Obviously the alumni are composed of factions, and presumably a large fraction of the potential participants are also members of other organizations with latent power networks and participating in this particular situation would involve expending capital in these other networks with potential reduction in power. Some alumni that have spoken up (i.e., Ackman) are clearly unaligned with the current coalition, and this MAY reflect the fact that the wealthy/powerful group of alumni that have sustained Harvard are really unhappy with the current stances of the university and would like it to shift (return?) to a different set of ideologies. But it's also possible that he represents a minority, and the rest are just nervous about getting involved.
My conclusion from this analysis is that things will persist as they have, with everyone who might be involved hoping that lawsuits will be successful in resolving the situation with the minimum of their involvement. If this approach is unsuccessful, I think we'll end up in a situation where we get a much better observation of the power balance between alumni, faculty, and board (I think the students rarely have as much power as they think they do!).