What should be administered next if sympathomimetics fail to relieve symptoms in an asthmatic patient?

When sympathomimetics, such as short-acting beta-agonists, fail to relieve symptoms in an asthmatic patient, the next step in treatment is to administer systemic corticosteroids like methylprednisolone. These medications are effective in reducing airway inflammation and can help in cases where bronchospasm persists despite the use of bronchodilators.

In acute asthma exacerbations, if the first-line treatment does not lead to adequate symptom relief, it indicates a more severe level of airway inflammation possibly contributing to the severity of the attack. Methylprednisolone works by downregulating the inflammatory response, thus addressing the underlying pathology of the exacerbation.

Other options, such as leukotriene modifiers and salmeterol, are generally used for long-term management or as adjunctive therapy but are not typically indicated in an acute setting where immediate relief is needed. Beta-agonists, while effective as bronchodilators, are the class of medication that has already been tried and failed in this scenario. Hence, advancing to systemic corticosteroids is the appropriate step to manage the asthmatic patient effectively.