Website says:
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Battery life Approximately two months of continuous shooting with a delay of 5min, an exposure time of 4min 56s, and an interval of 5min. Use of the illuminator will reduce battery life.
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It is not clear for which set of batteries they claim the life.. For remote part (AA?) ?
Probably your sample is faulty (try to measure the current with multimeter).. or replacement batteries were old?
I have similar gadget (in appearance.. and not wireless, it uses CR2032), battery last for months or years.