How does Rita Vrataski find out that she lost her power to "reset" her day without killing herself?

She states in the movie that after she received a blood transfusion she could feel the ability had left her. Cage also notes this when he wakes up in a military hospital after a botched attempt to retrieve the transponder prototype, as the result of a blood transfusion.

As such, it would seem the ability is something you can feel, and thus you can tell when you've lost it.

Rita Vrataski (Emily's character) and Cage both state the same thing. They simply felt it gone. Some senses, feelings, or states can be felt intuitively. Like being drunk or a hang over, you just know when it's gone. The Alpha blood must impart a feeling like that as part of it's power. As Full Metal explains to Cage the only rule:

Rita: Now listen carefully. This is a very important rule. This is the only rule. You get injured on the field, you better make sure you die.
Cage: Why?
Rita: Last time I was in combat... I was hit. I was bleeding out. Just not fast enough. I woke up in a field hospital... with three pints of someone else's blood and I was out. I lost the power. Do you understand?

After the crash, when Cage is tied down, and Rita, having escaped in 3 minutes flat, is about to kill him to trigger a reset:

Rita: Sorry, Cage. [Pulls out Gun to Shoot Cage]
Cage: No! Whoa. Wait! Wait!
I'm out. I'm out. They gave me blood.
I lost the power. I feel it. I can't reset the day anymore.

Considering Rita does not argue with him at all, and immediately starts planning their next steps, it's obvious that she knows what he means. She simply felt the power was gone.

Remember, the power comes with a mental component, psychically linking the Alpha (Rita or Cage) to the Omega. It's this intense feeling that is gone that lets them know it happened. Rita, as smart as she is, quickly surmised that her blood loss, like the dead Alpha's blood loss, leads to loosing the power.

In the comic that the movie is based on, "All you need is Kill", Rita and Kenji (Cage's counterpart) still retain the power until the end. They do not lose it by blood loss/transfusion, and the ending is completely different.

At some moment she received blood (Verdun's battle end; she mentioned in Edge of Tomorrow that Alphas were trying to find her 'cause Omega felt it lost its power to restart the day, btw: Cage was injured but not killed by alpha on germany's dam). Lather she died (battle, trining accident, etc), and she received RCP, when she "waked up" she realized that day wasn't restart, the fact that whent different is that she received blood and it was just a matter of time to conect the dots. May Dr. Carter tested the transponder (it was developed 'cause Rita's power), so they located the Omega, but it doesn't work again or may never when they attempted to find it again (Verdun was a false flag). That's why they knew that they needed an alpha and Rita lost her hability.