What is the point of political repression except short term power
Why do you think that short term power is not important enough to justify (in the government eyes) the repression?
We are not talking about stablished democracies here. If the ruling party loses power, the new ruler will repress it, it is not as if they will be able to present to the next elections in 4 or 5 years. Losing power in the short term may lead to never regaining it, exile, jail time or even death. That is pretty much of an incentive.
Now a couple of points:
- Hoping for better times. As good as "democracy" and "freedom" sound, protests tend to be more pragmatic. Usually only a minority of protesters are highly ideological, many others are compelled to act due to more mundane things (low standard of living, etc.) A government may try to keep things under control by means of force hoping that, in a few years, economic conditions will improve and the tension will ease. That explains why there may be revolts in Syria or Egypt while Saudi Arabia remains completely calm.
Now, about the possibility of just accepting the protesters demands, we can divide them between political demands and social/economical demands.
Political demands usually are those more difficult to accept. Maybe the protesters do not want to oust your government, only free speech or no censorship. But once these are met, future protests against your government will be easier to appear and more powerful. Definitely nothing the dictatorship can agree with.
Social and economical demands might seem more reasonable, and sometimes may be granted. But governments are not alone. Even dictatorial governments work because they have the support of at least part of the power base of the country, and they work for that power base. If people protests because they want higher salaries it might be tempting to take the peaceful stance and increase the salaries by law... until the people that will pay those salaries decides that the current government has lost its utility and change their support for another faction that is more compliant to them.
TL;DR; In the end, the price to pay for losing power is too high, so governments chose to rule by whatever means they have (including rule by fear). That does not mean that they want to do so or that they do not know of the risks, but they resort to the only solution left to them hoping for things to improve in the future.
And sometimes it works, you can see examples for Franco's and Salazar's dictatures in Spain and Portugal.
The youtube video pointed out by user4012 gives more information about the subject, although I find it a little too generalistic (e.g. it does not take ideologies or previous circunstances into account, ethnically based governments, etc.).