The W-1000 doorbox is designed to be connected to a Foreign Exchange Office (FXO or trunk input) of a phone system, or an ordinary telephone. It generates line voltage and AC ringing signal to call the phone system or ordinary telephone.
It is designed to interface directly with an unused analog telephone
line input of phone system. ... When the “Call” button is pressed, the
W-1000 generates a standard or custom ring cadence of an adjustable
number of rings.
https://www.vikingelectronics.com/products/w-1000/
I think it's likely that you have connected it to a Foreign Exchange Station (FXS) or extension port on the ATA which is intended to connect to a standard phone with loop connect, and which also generates line voltage AC ringing to ring that phone.
In effect, you've created two phone lines together, not a line and a phone. You probably need to connect the W-100 to a FXO or 'line' input on the ATA, and not the 'phone' connection, then set the 'line' connection to forward the call over IP when it receives an incoming ringing call.
Every time the W-1000 sends a burst of AC ringing voltage to the ATA, the ATA is probably registering that as a hang-up and new call request.
If you can't change the ATA, you probably need to change the W-100 doorbox to a model that mimics a plain old telephone eg
https://www.vikingelectronics.com/products/e-10a/
The E-10A is a telephone line powered door entry phone designed to
provide two-way handsfree communication. When the “Call” button is
pressed, the E-10A will come off-hook and will remain off-hook until a
CPC signal is detected, the programmed timeout has elapsed, a busy
signal is detected, or the call goes silent, making the unit
automatically disconnect.
The E-10A can be used with a Viking K-1900-5 or K1900-30 dialer, or
connected directly to a CO line or analog PABX / KSU station when
programmed as a ringdown circuit.
This video explains the difference:
https://www.vikingelectronics.com/fxo-vs-fxs-ports-know-the-difference/
Alternatively, you can use a Viking C-1000B controller between the W-1000 and the phoneline/ATA.
https://www.vikingelectronics.com/wp-content/uploads/documents/product_manual/W-Series.pdf