The premise of the strategy is that the convertible is sometimes priced inefficiently relative to the underlying stock, for reasons that range from illiquidity to market psychology.
However, maintaining a market-neutral position may require rebalancing transactions, a process called dynamic delta hedging.
For example, many convertible arbitrageurs suffered losses in early 2005 when the credit of General Motors was downgraded at the same time Kirk Kerkorian was making an offer for GM's stock.
[1] However, recent studies find empirical evidence that convertible bonds usually generate relatively large positive gammas that can make delta-neutral portfolios highly profitable.
"A simple and precise method for pricing convertible bond with credit risk", Journal of Derivatives & Hedge Funds, 19 (4), 259–277.