In principle, covered call is a bullish strategy where owner wants to own the stocks (so that stocks are gaining value) and at the same time, wants to collect monthly rent on stock asset.
In bearish market, the value of underlying stock might fall more then the premium collected by selling covered option.. which ultimately results in loss. So, better to avoid in bear mkt or modify the approach and cut Stock position with Stoploss.
I used this strategy during bull market with +ive result but dropped it after getting confirmation of bear market by Feb-08 (and also few loosing trades).
Happy Trading.