Though they almost never participate in direct physical combat, a Kekkaishi's duties require them to have above average physical conditioning.
Because they must often scale walls, trees, buildings, and other tall obstacles, a good sense of balance is very important for a Kekkaishi. They sometimes pursue targets (and each other) over rooftops, using their above-average leaping ability to cover ground quickly. As the series progresses, Kekkaishi are increasingly seen perched upon mid-air Kekkai without any signs of discomfort.
While on duty, the average Kekkaishi spends over half of their time running: either pursing their targets, or avoiding attacks. Comfortable, long-lasting footwear figures heavily into their uniform, and something as simple as a broken sandal strap could not only be unlucky, but quite dangerous under the wrong conditions.
Kekkaishi must have excellent reaction time, both in terms of how fast they can dodge enemy attacks, and how quickly they can produce Kekkai in the midst of combat. Yoshimori greatly improves his reflexes by training against local crows.
A Kekkaishi's strength is generally measured by the power of their Kekkai, as they almost never engage in direct physical combat. Greater power tends to translate into stronger and larger Kekkai, as well as the ability to produce and/or collapse large numbers of Kekkai rapidly. Sumimura in particular have a talent for producing very large Kekkai.
Endurance is a highly important factor for an on-duty Kekkaishi. Because they usually have no idea how many enemies they will face on any given night, careful conservation of power is both recommended and sometimes mandatory. Yukimura Kekkaishi especially practice this, and it is something that Tokine repeatedly scolds Yoshimori for ignoring (though in his defense, Sumimura Kekkaishi tend to have excellent endurance as a rule, and Yoshimori never seems to run out of power as another).