Tadayoshi,
The manual states very few things about batteries except when replacing to observe the correct polarity. There are protection diodes in place to prevent reverse current from destroying the circuits but one would not want to test this.
The second caveat refers to continous memory. The continous memory in the HP 41C and 71B is maintained during a battery change by a capacitor which, according to HP will discharge in 30 to 60 seconds, at which time the memory containing, programs, registers and calculator state will be lost. In practice this capacitor can maintain the calculators memory for up to 24 hours as long as no keys are pressed or the 'on' switch is selected.
In some locked up calculators the procedures listed by HP in order:
1. turn the calculator off and then on.
2. hold down the back arrow key while selecting on (master clear)
3. remove batteries and allow calculator continous memory to
discharge over night
Next are users discovered procedures (used at own risk) and used only after HP's steps above have been followed to no avail:
1. reverse the polarity of the batteries (don't like that one)
2. short out the battery clips (watch for static discharge)
3. while the batteries are out, to speed up the capacitor
discharge press the on key a few times.
All of the above steps are used to clear a non functional calculator state that is being preserved by continous memory. The assumption is that whatever locked the calculator up is being retained in continous memory.
Now to your problem, never as Plasmoid states (although if you forget, don't worry) remove modules or charger/wall wart power supplies while the calculator is on. Always select off first before doing anything physical such as adding or removing modules. It is very rare indeed that the mistake of leaving the calculator on during module changes will result in a dead calculator, I know as over the last 28 years I have made that error without damage.
Merely removing the batteries and storing the calculator should NOT cause damage and a prolonged restart of the calculators as you describe. After 28 years with my 3 HP 41's and recently with my two HP 71B the process of removing the batteries has never caused a restart as you describe. Also, the 41's and 71B have been in storage for years without batteries and again start up immediately, albiet in a 'Memory Lost' condition.
When you purchased one of these calcs off the shelf they may have been sitting for a few years in the box without batteries and are designed to start up immediately upon the correct insertion of the batteries.
Also, the HP 41C, and CX manuals along with the HP 71B user manual state nothing about 'trauma' or 'start up delays' when the batteries are inserted correctly after the calculator has been sitting for a long time (at the time of purchase or after storing with no batteries installed).
So from your original post, NO, a delayed start up as you describe is NOT normal for the HP 71B or HP 41CX. They should at worst start in a 'Memory Lost' state within seconds of the on switch being selected, regardless of how long they have sat without batteries.
If the worst that occurs is the delay in start but the retention and correct functionality of the calculator is normal after that, then you are lucky. I will leave the analysis of the circuitry causing the abnormal delay in start up to the circiut gurus resident at this site.
Cheers, geoff
Edited: 4 May 2008, 4:08 p.m.