I found the manual for your elite 4x DSI at
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On page 23 input voltage range is 10 to 17 volts.   The current draw is 200mA = .2 Amps. We will assume that the detector always draws 200mA.  This means that if you have your detector on for 2 hours it will use ( 2 hours X .2 Amperes = .4 Amp hours) .4ah.
I do not have the lithium data so I will use ultra-alkaline AA.  Data is available at
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You have 8 batteries in series and these batteries put out 1.6V when new. 8X1.6 = 12.8 Volts.  The elite needs minimum on 10 volts to work properly (probably does not shut off till it gets down to 8-9 volts but does not work well below 10 volts).  10 volts divided by 8 batteries ( 10/8 = 1.25) means each battery must supply 1.25 volts for your detector to work well.  Look at the graph on the first page of the above Duracell web site.  The .2A load is closest to the blue line(.25W). Follow the blue line to where it crosses the 1.25 V line.  Ok there is no 1.25 line so go between 1.2 and 1.5 and from that point drop straight down and you will see 4 hours service.  That battery will supply .2A current draw for about 9 hours but in a 8 battery system you do not have enough voltage. 
Lets do that over with 10 batteries in series. 10 batteries in series at 1.6 volts gives 16 volts which is below your manual max voltage. 10 volts divided by 10 batteries means each battery must supply 1 volt for the elite to work properly.  Go back to the chart on the Duracell site.  Follow the blue line down to 1 volt then drop straight down and you get a little over 9 hours.
Lithium batteries are a little higher voltage and you want 9 batteries in series with Lithium.
I do not have discharge curves on the battery that was in my previous link but if it is over 10 volts when it is at it rated ah then you could get 25 hours with your elite.  This battery weighs 18.6 oz. This is a Lithium Polymer ( also called Lipoly) and they require special chargers.