Battery voltage drops suddenly

[mzsk07]

Why do 1 of my 2 6v batteries connected in series in a rechargeable fan fail within days? One battery drops to 2 volts within one minute when load is turned on, and then very slowly goes back to 6v once load is turned off. This problem starts in 10 days after replacement with new batteries. Only one battery fails.

[ClassicCrazy]

What kind of batteries are you talking about ? What is the load of the fan , age of batteries, etc ?  How deep are you discharging the batteries from full ?
Were the batteries fully charged after you got them ? How often are you charging them ?   Also it can take a few cycles to on lead acid batteries to get them to full capacity .
There are so many factors that need to be considered so that is why I ask all the questions. 
If flooded lead acid batteries they may need equalize since one or more cells may be low.

Larry