>>49810009
A tsukumogami comes into existence due to spite/sorrow around the fact that they've been forgotten and aren't needed. Kogasa is a happy umbrella, and she's found a new purpose (several in fact), you loving her would give her another purpose and she'd stay with the umbrella to keep having a purpose, the umbrella gives her her form, doesn't it? That's her body.
Technically, you can drive her spirit out of the umbrella, and turn it back into a normal object, but Kogasa would still exist, just as a spirit.