The Or LaShamayim (באר עלי ה"ד חוקת) answers in the name of the Chozeh of Lublin zt'l that there is more than one akeidas Yitzchak. Whenever a person overcomes his yetzer hara, it is considered an akeidas Yitzchak. The Chozeh explains the pasuk as follows: אחר איל והנה, there are other akeidas Yitzchaks. בסבך נאחז, when one is trapped in the lure of temptation and bad habits, and he overcomes them, it is another akeidas Yitzchak. בקרניו, the Or LaShamayim explains, can also mean “shine” (as in Shemos 34:35, פניו עור קרן כי, Moshe's face shone). When one passes his tests הכבוד כסא עד אורו תהל, "His light shines up to Hashem's throne."
It is encouraging to know that we can perform an akeidas Yitzchak even in our times. Whatever level you are on, when you overcome your nature and take a step forward, it is a sacrifice, an akeidas Yitzchak. In Shemoneh Esrei of Rosh Hashanah, we say, תזכור היום לזרעו יצחק ועקדת, "Remember akeidas Yitzchak today..." We can explain that we ask Hashem to remember the akeidos that happen today, and every day, when we overcome the yetzer hara.
The Shlah Hakadosh on Modern Akeidas Yitzchak
The Shlah Hakadosh (ב"מ אות מוסר תוכחת חיים דרך וירא) elaborates on how to perform an akeidas Yitzchak in our times. He writes: "When we think about the self-sacrifice Avraham and Yitzchak displayed at the akeidah, we derive mussar that we, too, should be moser nefesh for Hashem. Certainly, one should be able to break a taavah. For example, to wake up early for Torah and tefillah or to refrain from pleasures, idle talk, and so on. One should forgo his will to do Hashem's will. If an aveirah comes his way, or a mitzvah, he should think, 'Perhaps Hashem is testing me now, similar to the test that Hashem gave Avraham. Because when a person knows that Hakadosh Baruch Hu is testing him, he will be cautious. Whenever a test arises, remember that it is Hashem that is testing you. Fortunate is the person who always keeps Hashem in his thoughts.'"