If a person had a seminal emission from masturbation and did not go to the mikveh how long does this person remain considered impure for. Is the only way to become pure again through going to the mikveh.
כָּל הַטְּמֵאִין בֵּין אָדָם בֵּין כֵּלִים בֵּין שֶׁנִּטְמְאוּ טֻמְאָה חֲמוּרָה שֶׁל תּוֹרָה בֵּין שֶׁנִּטְמְאוּ בְּטֻמְאָה שֶׁל דִּבְרֵיהֶן אֵין לָהֶן טָהֳרָה אֶלָּא בִּטְבִילָה בְּמַיִם הַנִּקְוִין בְּקַרְקַע:
Whatever is defiled, whether human beings or utensils, whether rendered unclean by some grave uncleanness on biblical grounds or by some uncleanness on rabbinic grounds, can become clean only by immersion in water that is gathered on the ground [not within a receptacle].
So, in short, yes. The only way to become pure again is through going to the mikvah. Otherwise, he remains impure indefinitely.
That being said, this is all of limited relevance today. As a matter of halachah, there is no problem for a man nowadays to choose to remain in this state of impurity indefinitely (unless he is planning on visiting parts of the Temple Mount in Jerusalem).
Although there used to be a rule limiting the participation of one who had a seminal emission (ba'al keri) in reciting various parts of the liturgy and studying Torah before he immerses in a mikvah, Shulchan Aruch (Orach Chaim 88) rules:
אף בעל קרי מותר בד"ת ובק"ש ובתפלה בלא טבילה ובלא רחיצה דתשעה קבין וכן פשט המנהג:
Even the ba'al keri is permitted in Torah, reading the Shema, and prayer, without immersion and without washing with nine kab of water, and such is the custom.
Mishnah Berurah 88:4 notes:
ומ"מ יש אנשי מעשה שנוהגין בתקנה זו וטובלין א"ע לקריין ואם קשה עליהם הטבילה רוחצין א"ע בט' קבין
Nevertheless, there are pious people who are accustomed to keep this ordinance, and immerse themselves after a seminal emission, and if immersion is difficult, they wash themselves with nine kab of water.
So, if one has the custom of not praying after having had a seminal emission, then washing oneself in nine kab of water, rather than going to the mikvah, is an acceptable manner of keeping this custom, if going to the mikvah is difficult.
Actually, going to the Mikveh isn't sufficient.
As the Torah informs us in Devarim 23:11, he has to go to the Mikvah and after sunset of that day (that he goes to the Mikveh) and then he finally becomes purified.
כִּי־יִהְיֶה בְךָ אִישׁ אֲשֶׁר לֹא־יִהְיֶה טָהוֹר מִקְּרֵה־לָיְלָה וְיָצָא אֶל־מִחוּץ לַמַּחֲנֶה לֹא יָבֹא אֶל־תּוֹךְ הַמַּחֲנֶה׃
If anyone among you has been rendered unclean by a nocturnal emission, he must leave the camp, and he must not reenter the camp.
וְהָיָה לִפְנוֹת־עֶרֶב יִרְחַץ בַּמָּיִם וּכְבֹא הַשֶּׁמֶשׁ יָבֹא אֶל־תּוֹךְ הַמַּחֲנֶה׃
Toward evening he shall bathe in water [of a Mikveh], and at sundown he may reenter the camp.
As Rashi (ibid) explains:
והיה לפנות ערב. סָמוּךְ לְהֶעֱרֵב שִׁמְשׁוֹ יִטְבֹּל, שֶׁאֵינוֹ טָהוֹר בְּלֹא הֶעֱרֵב הַשֶּׁמֶשׁ (עי' ספרי):
והיה לפנות ערב BUT IT SHALL BE WHEN EVENING COMETH ON, [HE SHALL LAVE HIMSELF WITH WATER] — He should immerse himself close before the setting of the sun, for under no circumstances is he clean without having waited for the sunset (cf. Sifrei Devarim 256:2).
All the above refers to his state of impurity, preventing him from entering the Bet HaMikdash and eating Korbanot.
There was a Takanat Ezra that forbade men who had emissions from praying. This Rabbinic impurity disappeared after going to Mikveh (without the need for waiting for sunset).
In cases of need (like sick people), having 9 Kav (~13 liters) of water poured over oneself (e.g. a long shower) would suffice.
This edict - Takanat Ezra - was canceled by later generations and no longer applies, though some are stringent to abide by it when possible. (E.g. not on Yom Kippour).
See Rambam, the Laws of Kriat Shma 4:8 for details