Take a page from video games and treat your personal best streak as a high score.

Classic games like Pac-Man show your high score at all times as a goal to reach, and when you achieve it you get to see both numbers change at the same time to reinforce the fact that each point is setting a new record.

More recently, Diablo 3 offers increasingly elaborate frames for your character's portrait as you level up. It's a small but tangible reward that visually reinforces your progress and provides additional incentive to get to "better" frames or just to see what comes next.

Rock Band not only tracks a high score, but also various levels of "stars" that get filled in when your score crosses various thresholds. (On the middle right, below the score.)

Some games like Geometry Wars that are all about chasing higher and higher scores will also show the high scores of your friends next to your own. This can serve as bragging rights, or provide incentive to try a little harder when you see your own top score trumped by someone else's.
Here's quick mockup using some of these ideas:

- Make the current streak count larger since it's most important.
- Show the "high score" on the screen as a goal to reach.
- Use smaller units for good numbers and larger units for bad numbers.
Measure the current streak in days so that you can see it tick
over into double, then triple digits, but measure the time to catch
up to the personal best in weeks or months so the numbers are
smaller.
- Change the image, color, or shape of the badge around the number as incentive to keep the streak going. It's a small reward, but checking back every day to see how things change can create a feedback loop and you'll have a rudimentary Skinner box.
- Consider having additional week or month counters that fill up over time as the streak reaches those thresholds. The visual feedback of a nearly full container and the perception of a sunk cost (in that they've come to far to give up now) can be a powerful psychological force.
- Only have a single button to keep the streak going. No one wants to admit failure and making them manually press a button to wash away their hard work is a little mean. Either they'll cheat and not press it, or they will and feel mad at the app. It should be enough to have them check in at regular intervals and hit the button to keep the streak going. If they fall off the wagon and avoid using the app out of shame, that should be enough to break the streak. (You should offer encouragement when they have the courage to return to the app and start a new streak.)
- If your app has a social component, consider adding the streaks of the user's friends as well as their own. This could allow you to use peer pressure as a positive force.
There are many other game concepts you could use like multipliers or "ghosts" when trying to catch back up to your previous record. But be careful you don't go too far down the gamification path. It will be hard to do successfully when the rewards (better health) don't fit inside the game system loop.
Pac-Man image from http://www.arcade-museum.com/game_detail.php?game_id=10816
Diablo 3 Paragon portraits from http://diablo.wikia.com/wiki/Paragon
Rock Band image from http://en.wikipedia.org/wiki/Rock_Band
Geometry Wars scores from https://pokehface.wordpress.com/2010/11/