Are you using a 3rd Generation (or later) Xbox One controller that has the Bluetooth support option? If so, how is it connected to your PC (ie wired USB connection, wireless XBOne receiver dongle, or via Bluetooth)? Do you have a single Bluetooth receiver and what is its model and Bluetooth version support (ie is it a BT USB dongle that supports Bluetooth 4.x , part of your motherboard or laptop's wireless chipset and supports Bluetooth 2.1 etc)?
In addition, do your BT earbuds also have an option to connect via a wired 3.5mm jack?
In the event both devices are connected using Bluetooth, I would suggest the first thing is to try connecting one or both of them via a wired mode, if applicable. See if the issue still continues. If it does, there may be something else going on, but if everything works fine with at least one of them in wired mode , then it sounds like a Bluetooth issue either with the dongle at "capacity" so to speak or perhaps congestion on the spectrum. This can be mitigated by A) using something in wired mode which you may not wish to do B) using multiple USB Bluetooth dongles which can sometimes deal with temperamental devices (though this won't work if there is actual spectrum congestion/overlap between the two) or C) Buying an Xbox One wireless receiver like this one - https://www.amazon.com/Xbox-Wireless-Adapter-Windows-10/dp/B0785RHK5Q/ - which connects using a different protocol entirely compared to Bluetooth. Please note that I linked what seems to be an authentic version of the XBOne PC wireless receiver and is the newest variant - the 2018 edition, as compared to the larger, flatter 2015-era edition. Both are viable, but the one I linked is known to be a bit upgraded so its worth the investment if making a new purchase.
Hope some of this can help.
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