How do I tell my elderly mother that I can’t stay for long visits?

Good observation on your part, to distinguish that your feelings in relation to your mom are not necessarily connected to the way she handles her part of the relation toward you.

Has your mom usually ignored your opinions and wishes in relating to you?

If prior to the onset of Alzheimer's, she never examined her way of relating to you, and if both of you have never had an open conversation about your sense of feeling hurt by her attitudes and manner with you, then the relationship between you and your mom will change in ways other than rational dialogue.

She may continue ignoring or overlooking your wishes because she's been stuck in this attitude for most of your life.

The good news for you about this is realizing that who you are and your way of relating to your mom, has very little to do with the way she relates to you.

This is a more profound disappointment because it shows that her disconnect from you has been for longer than when the Alzheimer's began.

You can however, feel a little more free knowing that you're not deserving of being ignored.

There are many conflicting emotions and tasks that arise when one becomes a caretaker for their parent. 

Expressing positive emotions to her (i.e. "Mom, I love and care for you, and enjoy our time together. I'm sorry I can't stay long"( may help re-frame your thoughts and have a fresh perspective on the situation. Additionally, Visual cues like pictures and notes can also be helpful for those who suffer from disorders like Alzheimer's and Dementia, as it offers a "Trigger" for memory, helping to ease the doors to communication. 

Finding support in other family members, or a therapist familiar with elder care issues may be helpful as well.