1994 jeep starting problem

when this jeep sits for a couple of days it will not start. alt is charging ,batt is good,when you jump it it starts right up. I noticed the other week a new beeping sound about 30 sec after you start the jeep ,does anyone know what this could be ,the infomation center does not say anything is wrong. A while back I had a draw on the battery and when I pulled the IOD fuse the draw whent away,I fixed that problem can anyone help with this problem? thanks so very much in advance.