You have to talk to her. If you lose your job, she will lose hers too. If she is great every other way you don't want to lose her, but if she isn't there it really doesn't matter how great she is, does it?
Can you go by the attendance policies that a company would normally have?
At my last place of work we had to track attendance. Coming in late counted as a half occurrence, missing a half day or whole day counted as a whole occurrence. When the person got up to a total of 6 they got a written warning. A written warning lasted for 6 months. If there were no more absences during the 6 months the notice would be taken out of the personnel folder.
After three written warnings in their folder they were dismissed at the next absence. Even though someone would need to come in late about 36 times to be fired, there were still people who did so, and were.
In case this sounds heartless, if they had a good reason for absences the manager would usually work with them to help resolve the situation. I had a single mother working for me who was always late in as she had to take her children to the sitter. I just moved her shift hours so she was no longer late as it worked for my department.
Personally I would be heartbroken if my pet died, but I would still go into work. Similarly we would have been given 3 days off if an immediate relative died, but a cousin, aunt or uncle would have required vacation time to attend a funeral.
Maybe start this thread again in Employment issues to find out what the norm is for attendance at a place of business.
You have to decide whether she is your friend or your employee. Given that your job depends on her doing her job, I think you have to go down the employee route and treat her accordingly.