According to a study from Canada, the wait time does not appear to be a risk factor for a poor result. Gender, age, and health are the biggest indicators of outcome.
For example, older men seem to have worse results when a second operation is needed after a hip replacement. Both men and women with other health problems are also at increased risk for more pain and less function after the operation. Diabetes, hypertension, heart disease, and cancer are just a few of the conditions that can contribute to a poor result with revision surgery.
One other factor is important in predicting the outcome of revision surgery for a loose or unstable hip replacement. The level of pain and physical function before the operation are key factors. Higher levels of pain before is often linked with greater discomfort after.
All this aside, your mother may have a perfectly normal recovery with no problems whatsoever. The time she waits may contribute to her deconditioning but shouldn't affect the results of the revision operation.