Do you need to stop a beta blocker before a drug challenge? Food challenge? For how many days? What about an ACE inhibitor?

It is generally advised to stop medications that may increase the risk of anaphylaxis before any procedure that may induce anaphylaxis. Such procedures include a drug challenge or an oral food challenge. The medication should be stopped for enough period of time to allow for 5 half lives to pass after the last dose.

For example, the elimination half-life of oral atenolol is approximately 6 to 7 hours. Atenolol should not be detectable after 5 half lives, 5 x 7 hours = 35 hours (1.45 days).

From the EAACI guidelines:

Concomitant medications and pretreatments

Before beginning any desensitization procedure, patients should be in a stable clinical condition (e.g., FEV1 ≥ 70% of the normal value for asthmatics, controlled cardiac insufficiency). Any concomitant medication used for treating underlying diseases must be continued. However, drugs such as beta-blockers, which can interfere with the treatment of a severe hypersensitivity reaction, should be discontinued whenever possible. Indications should be strictly observed, e.g., sudden withdrawal of beta-blocker therapy in patients with arrhythmia may be life threatening.

Contraindications

Desensitization to culprit drugs should generally not be performed in patients at increased risk because of a co-morbidity, such as those with uncontrolled asthma (FEV1 < 70% of their normal value), hemodynamically unstable ones, or those with uncontrolled cardiac diseases. In patients treated with beta-blockers and subjects who have experienced severe anaphylaxis, as well as in patients with hepatic, renal, or other diseases, in whom exposure might provoke a potentially harmful complication, desensitization should also only be considered after a careful individual risk/benefit evaluation. Desensitization is absolutely contraindicated in patients who have experienced severe, life-threatening immunocytotoxic reactions, vasculitis, or bullous skin diseases like SJS/TEN, and DIHS/DRESS.

I did not find guidelines on ACEI inhibitors.

Related reading:

General considerations on rapid desensitization for drug hypersensitivity – a consensus statement. Allergy, 2010.
http://onlinelibrary.wiley.com/enhanced/doi/10.1111/j.1398-9995.2010.02441.x/

Immunotherapy with ocular beta blocker. AAAAI Ask the Expert 2015.
http://www.aaaai.org/ask-the-expert/immunotherapy-ocular-beta-blocker.aspx