As part of the diagnostic procedures, the man might be required to undergo Testicular Sperm Extraction, or TESE. The procedure presents serious halachic challenges.
TESE (testicular sperm extraction) involves multiple fine needle biopsies to remove tiny samples of tubules containing sperm. This procedure is usually performed under a local anaesthetic and takes about 30 minutes to perform.
Under some circumstances, the procedure might involve actual surgery if the above method is not effective.
The Torah in Deuteronomy 23:1 prohibits a man with any injury to the testes from marrying. The Gemara in Yevamot includes in this prohibition any wounding of the penis, testes or cords of the testes. As such, the performance of this procedure might be considered in halacha as p'tzu'a dakkah and make continued marriage halachically unacceptable. Indeed, The Z'kan Aharon rules stringently.1
Given that the injury will in all likelihood heal, and, likely as not, result in enhanced fertility, Rabbi Moshe Feinstein permits TESE and similar procedures such as testicular biopsy2. Moreover, the Minchat Yitzchak rules that the prohibition only applies in the first place to a man with clear reproductive capacity3. Under the circumstances, the patient in this case cannot be described as such.
Any procedure that involves injury to the testes risks transforming the husband into p'tua dakkah. Although stringent opinions do exist, Rabbi Moshe Feinstein, among others, permits TESE.
1. Z'Kan Aharon Vol. I, 66.
2. Iggrot Moshe, Even Ha'ezer Vol. II, 3:2.
3. Minchat Yitzchak Vol. III, 108:7. See also Tzitz Eliezer Vol. IX, 51:1.2.