I have tested the following Logitech mice over the last 2 years (This information might give you an idea on how to test the mouse yourself and solve the problem):
- T620 Touch
- Anywhere MX
And I can say the following:
T620 Touch - Everything works in Ubuntu. From side scrolling to both buttons. From zooming to double clicking. The distance is the best out of the 4. The only problem is that it does not have a middle button.
Anywhere MX - Excellent mouse. The side buttons, 2 middles buttons and fast scrolling make it the most used one I have. The horrible problem is that it uses the batteries at least 3x faster than any other AND the distance is horrible. Less than a meter. I had to send it back and change it for a new one. After about 4 months the problem started again.
M555B - Excellent mouse and I like fast scroll it has BUT here are the problems you might be facing:
Power problems. The first one I had, I used new batteries (Tested the batteries in the T620 before using them in the M555) and somehow it did not work correctly. A lot of stuttering or simply going off after about a minute. At first I thought it was the Bluetooth (A Kesington 2.0) but it was working great with my Samsung S4. I then tested the M555 with the Samsung S4. It did not work. So I send the mouse back saying it had a bluetooth issue. Got a new one about 2 months later.
Bluetooth issue. It might be a BT issue with the mouse as mentioned above or with the BT of the computer. Test the BT with a phone or another BT device to see which one is the problem.
What I would recommend is that you connect the M555 to a phone or tablet that has BT support. If it works correctly then you know the problem is in the BT of the computer. If it does not, then it is the actual mouse the problem.
If the problem happens to be the BT of the computer then you can check which version of BlueZ you have. If you are in 13.10 it should be the 4.101. In 14.04 I do not know (I hope it will be the 5.17 that appeared yesterday since it will give support to a motherboard I have).
I would suggest compiling the latest BlueZ version and testing it out. The latest at least makes my BT of the computer (Asus Z87 Pro) work.
With this I am saying that Logitech are not very good with all products. Some will have some weird problems others will not. Apart from this, all Bluetooth devices or not working 100% yet (The latest ones). In the case of the M555B for me, I needed to change to another one to fix the problem. Tested on 13.10 right now.
To test what in the world is going on in your case I would first recommend doing the following (Does not matter if you do it before or after connecting the mouse):
tail -f /var/log/syslog
This will constantly display what is happening to the system. So after doing that connect or disconnect the mouse and try to pair it. Repeat at least 2 or 3 times with the working intervals you mentioned (2 or 3 minutes of working time). After you have enough logged information about what happens between connecting and the 2/3 minutes of disconnection, post that on http://paste.ubuntu.com and link it in your question or in a comment. This way we can do a follow up on it.