Can I leave the handsets in the base all the time or should I remove them once they are charged?

Multiple handsets registered to one base works well.
The extra base can be used as a remote charging
dock without registering a handset.

Trying to register a handset to two bases is neither
possible nor useful.

Good luck!
----------------

OTOH, the specific model number was
not given. While I have never heard of
registering a handset to more than one base,
nor made it happen by accident, maybe we
all do "...learn something new everyday...".

What is the specific model number, and the
date of manufacture ? Thanks! a r t
---------------------------------------------

Normally in the BT range the batteries are rechargable, hence the base charger, so do not use ordinary batteries. If the phones are not charging, go to boots or tesco and buy AAA rechargeables 2 per handset. Once replaced allow at least 6 hours charge before use. After that just carry on as normal.

• Your telephone can accommodate up to four cordless handsets. You can add new handsets (Model E560-2, sold separately) at any time, but each must be registered with the base before use.
• The handset provided with your telephone is automatically registered as Handset 1.
• Additional handsets will be assigned numbers in the order they are registered (2, 3 or 4). You can register a maximum of four handsets.

To de-register all handsets
• Unplug the power supply from the base unit.
• Remove all handsets from the charge cradles and base.
• Plug in the power supply while pressing and holding the HANDSET LOCATOR button.
• Continue pressing HANDSET LOCATOR until the IN USE and CHARGING indicators are lit (this could take up to 10 seconds).
• Release the HANDSET LOCATOR button.
• All handsets will display: ENTER BASE ID: XXXXXXXXXX
Once the base indicators turn off (up to 30 seconds), the handsets have been de-registered from the base, and can now be re-registered.

To re-register a handset:
• Make sure your handset batteries are properly installed and charged.
• Your handset will display "ENTER BASE ID".
• Enter the 15-digit Base ID number from the bottom of the base unit.
• Press SELECT to accept the new code and complete re-registration.

To re-register a handset to a new base unit:
• Make sure your handset batteries are properly installed and charged.
• Unplug the old base unit. Your handset will display "SEARCHING...".
• Install the new base unit by plugging it into an electrical outlet and phone jack.
• Press and hold the SELECT key until the handset displays "ENTER BASE ID".
• Enter the new 15-digit Base ID number from the bottom of the new base unit.
• Press SELECT to accept the new code and complete re-registration. The handset is now registered to the new base.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

This problem can be caused by the following, A bad battery, (which you say you are all new). A full base memory and a Faulty main base unit
This main base unit can only expand to four handsets and no more. If the base unit has been reset then the assigned numbers for each handset would begin with " handset 1" if they show any other number when reset then it would not have been reset..To re-set main base you will have to
De-Register All Handsets
Unplug the power supply from the base unit then Remove all handsets from the charge cradles and base then Press and hold the PAGE button on the base.
Plug in the power supply again while pressing the PAGE button, Continue pressing PAGE until the IN USE and CHARGING indicators are lit. (this could take up to 10 seconds)
Release the PAGE button All Handsets will display "enter base id".
If this does not solve your problem then you will have to replace the main base

*331734#Menu Select on the handset should de-register that handset from the old base, then you can register it to the base as per the manual (put it in the base and hold down the handset locator button for 4 seconds)

I took the post that mentioned removing the battery, waiting a few minutes and then reinserting it.  It worked.  Thanks to that person.

The handsets are reading out of range because they have lost connection with the base. This happens mostly during peak power demands or power outages, but can also happen when the phone is unplugged for any amount of time. This can also cause, at times, the answering machine to stop picking up calls. To remedy this issue, reset the phone system. Please follow the instructions below:
To reset the phone:
1. Disconnect the power adapter, phone line, and remove all batteries from the base and all handsets. Leave it disconnected for 30 seconds to reset the base.
2. Place the batteries in the handsets first and then plug in the power adapter and phone line. Do not place the batteries back in the base yet.
3. Put the handset in the charge cradle.
4. It may take up to 1 minute for the "Out of Range" to clear from the display.
5. Once the "Out of Range" is cleared from the handset place the back up batteries back into the base.

Help
My Bt Studio 3100 cordless telephone ( 2 Pack ). I have carried out the setting up procedures as per instructions.
Handset batteries are fully charged, but I am not getting the dialling tone.

Registering Handsets to the Base
Whichever handset you choose to charge in the base is automatically
registered to the base. Any additional handsets must also be registered to
the base before you can use them.
Be sure both handsets are fully charged.
One at a time, place each handset in the base. The charge/in use LED on
the base begins to flash, indicating the base is registering the handset.
Wait for at least five seconds, then pick up the handset and press
[talk/flash]. If the display shows TALK, the handset is registered. If not,
place the handset in the base to try again.
Press [end] and continue with the next handset.
Note:
Once both handsets are registered, it doesn’t matter which
handset is placed in the base or the charger.
When you charge the handsets, Caller
ID summary screen and the name of
the handset appears.

This can be find from uniden website.
http://www.uniden.com/pdf/DXAI4588-2om.pdf

Find the manual on the link below. Check batteries are charged preferably for a few hours then perform the reset as per the manual: To re-initialize the handset and base: 1 Disconnect the power to the base. 2 Remove the handset battery pack. 3 Wait at least 15 seconds. 4 Insert the handset battery pack. 5 Connect the power to the base. 6 Put the handset in the base to re-initialize. 7 Wait for handset to display READY (or handset name). http://telephones.att.com/docMgt/public/art/306/2255_.pdf