There could be two possibilities. When you press the flash button, your phone disconnects the line for a brief instant. Check the setting for the Phone port -> HookFlashTimeMax. Try setting it to a little larger value. I was having this same problem and ended up setting the value to 1250. Your phone may be disconnecting the line for just long enough for the Obi to think you have hung up and ended the call.
The second possibility is your firmware version. The Obi had a number of issues with call waiting and conference calls until they released the later V1.3 firmwares. I haven't had any issues using the flash button since I extended the HookFlashTimeMax and installed the newer firmware.
I'm already on the latest firmware so I'm guessing it's not that. I went ahead and changed the HookFlashTimeMax to 1250. I don't have much experience modifying the advanced settings of the obihai, so please let me know if I did it correctly:
Went into advanced settings of my obi110 via obitalk.com. clicked on phone, then unchecked "device default" and "ObiTalk" boxes that are to the right of HookFlashTimeMax, then replaced the value of 900 with 1250. I then saved.
Please let me know if I did that correctly. I'll go ahead and test this out to see if it resolves my issue. Thanks again for your help.