This one can be a real pain, I speak as one who has experienced this particular phenomenon more than once.

At some alleged haunted locations a perfectly new or fully charged battery can for no good reason become completely discharged in a few minutes and sometimes seconds. This can be a real problem if you are now in complete darkness and the battery concerned happens to be the one inside your torch. Tip; get one of those wind up torches and keep it in your pocket for just such an eventuality.

Tests have been carried out at some haunted locations using two batteries purchased at the same time from the same packet, both checked and found to be fully charged on a meter. One battery is in an investigators otherwise empty pocket as they wander about the haunted location, the other is stored outside the haunted area. Both batteries are subsequently tested again on a meter showing one to be fully charged, the other completely discharged without any obvious explanation why.

This phenomena has been proved to occur, what is not known is quite how or why  this happens and even if there is anything remotely Ghostly going on. If it were being discharged by a spirit it is not known how either a spirit or a  haunted location might be able to draw power from a battery or for that matter for what purpose.

I have come across on particular documented variation on battery discharge, which is interesting due to the range of otherwise sane people involved.
There was an occurrence where a family living in an isolated haunted farmhouse had widely varying electricity bills, up to £750 per quarter variation, which could not be explained by means of normal weekend only usage. The property is allegedly quite haunted, going along a believer route, maybe the uninvited guests present during the week found some way of using the mains electricity!

The sceptics view of this would be that this was simply a faulty meter, in fact this was my own first thought on hearing the account.

The problems with this explanation become apparent when you hear the rest of the story. The electricity company fitted a series of  replacement meters and faired no better. Eventually the electricity company carried out a full investigation and was unable to find any reason why so much power was being used by what was in effect a weekend cottage. Their equipment showed that electricity was being used when the house was empty and only during the night on odd nights.  Intruders? Or something else?

The family was advised to switch off the mains while they were away, which had no effect at all. Subsequently the electric company took out the main fuse for a week by agreement, yes you've guessed it the power was still being drawn, which is a little harder to explain away.

If anyone knows why or how power is drained from batteries at alleged paranormal locations answers please on the CaSPIR forum: http://www.caspir.org/forum/index.php