Who are the losers going to be? If you can tell me for certain which firms will do worst in a bear market and can time it so that this information is not already priced into the market then you can make money. If not don't try.
In a bull market stocks tend to act "normally" with established patterns such as correlations acting as expected and stocks more or less pricing to their fundamentals. In a bear market fear tends to overrule all of those things. You get large drops on relatively minor bad news and modest rallies on even the best news which results in stocks being undervalued against their fundamentals. In the crash itself it is quite easy to make money shorting. In an environment where stocks are undervalued, such as a bear market, you run the risk that your short, no matter how sure you are that the stock will fall, is seen as being undervalued and will rise. In fact your selling of a "losing" stock might cause it to hit levels where value investors already have limits set. This could bring a LOT of buyers into the market.
Due to the fact that correlations break down creating portfolios with the correct risk level, which is what funds are required to do not only by their contracts but also by law to an extent, is extremely difficult. Risk management (keeping all kinds to within certain bounds) is one of the most difficult parts of a manager's job and is even difficult in abnormal market conditions.
In the long run (definitions may vary) stock prices in general go up (for those companies who aren't bankrupted at least) so shorting in a bear market is not a long term strategy either and will not produce long term returns on capital.
In addition to this risk you run the risk that your counterparty (such as Lehman brothers?) will file for bankruptcy and you won't be able to cover the position before the lender wants you to repay their stock to them landing you in even more problems.