It's a common problem - the battery capacity is very low and there is no circuitry to protect against over-discharge which can occur in as little as two or three weeks if the radio is not used and which will quickly damage the battery. I have considered replacing the battery in mine, but it is a fiddly job. It's a surface mount device, physically small and not very accessible. I'm experienced at SMD construction and repair and have the proper equipment, but I'm nervous about doing damage to the main board.
If you do decide to replace it, it is a Seiko device. There is an alternative in the range which should be more suitable - it's designed to be more resilient to over-discharge. Alternatively, if you have your 7300 hooked up to a PC, there are a number of programs available that will set the clock for you. I control my 7300 via Win4ICOM and that has a function which will set the radio clock to the PC clock every time it is fired up. This is what I've chosen - too much risk involved in replacing it...
Martin (G8FXC)