How long can an ELT run before the battery is dead?
The reference you quote is correct as it defines the "useful life" of the battery.  that is: if you use it for more than 1 hour (that would include the cumulative test time) it must be recharged or replaced before being returned to service.  But that isn't what you are asking about.  You are asking for the duration of operation.

The requirement for Duration of Operation is 24 hrs.  

RTCA DO-204A, MOPS for 406 MHz ELTs, states


  1.5 Operational Goals  
  
  b. Operability  
  
  (1) The technical requirements of the 406 MHz beacon radiated signal
  are based on the COSPAS-SARSAT system.  
  
  (a) The 24-hour operating life requirement (§2.2.1) is based upon the
  maximum COSPAS-SARSAT system waiting time, the number of satellite
  overpasses required to optimize the beacon location solution and
  battery capacity limitation at low temperatures.


and


  2.2.1 Duration of Operation  
  
  Refer to COSPAS-SARSAT document C/S T.001.


and from C/S T.001  


  4.5.1 Duration of Continuous Operation  
  
  The minimum duration of continuous operation shall be at least 24
  hours* at any temperature throughout the specified operating
  temperature range. 
  
  The minimum duration of continuous operation for an ELT(DT) to meet
  the ICAO GADSS requirement at any temperature throughout the specified
  operating temperature range shall be 20† hours.