Fuzz:
What size cells are you using? By the sounds of the 1800mAh rating, your probably using AA's. I think Alkaline's have a higher amp-hour rating, but are very expensive and can't be "topped-off" to 100% before a dive like rechargeables. The reason you sometimes can't get away with rechargeables is the fact that they are only 1.25 volts. Alkalines are 1.5 volts. It depends on how much head-room the device needs before it stops workings. In the case of my UK H.I.D. light-cannon, it uses 8 c-cells. This is 12 volts on new alkalines (maybe slightly higher. But on rechargeables I'm only starting off with 10 volts. However, the discharge characteristics of rechargeables don't taper off gradually in voltage as alkalines do, but when they do, they avalanche in a real hurry. So you have to compare the longer life and higher voltage (initially) of alkalines, to the already "medium voltage" (but steady) and topping-off ability rechargeables.
In my case I decided against rechargeables, as the light output was noticably lower with 10 volts compared to 12. Not to mention the light dropped out at somewhere around 9 volts. I'm sorry if there is no clear-cut answer, but everything's a trade-off. First of all it helps to determine if the designer allowed for too much load for the amperage of the size batteries he chose. Maybe the draw is too high to get by with anything less than alkalines. Please include a little more info on the device, such as bulb type, cell size and count, and how much operating time you used to get with alkaline batteries. Hope this was of some use.
Jim