Safe? While you may have control at those voltages I wouldn't push it. The typical TX battery is 9.6v. Technically, anything under that and you should recharge. Most TX manuals will even tell you that the beeping for the low battery isn't the warning to recharge. You should have done that long before you hear that tone.

When you mean flying session, do you mean all day or just after one flight? If you're losing that much voltage after one flight you might need to either cycle the battery for the TX or get a new one. If you are losing that voltage through a whole day that is somewhat normal. If you're concerned you can always pull the battery and use a field tester with a load built in to test the battery. That will give you a good indication of it's output.

Hope this helps.