Supergirl fans, let's be real about this for a moment now that season 2 is nearing its all-but-inevitably Mon-El-related conclusion: The Prince of Daxam has seemed like a dead man walking since he first showed up in the premiere (well, technically he showed up at the end of season 1, as an unnamed/unseen offscreen character inhabiting the alien pod that crash-landed for the cliffhanger ending).
To review where we now are as of last night's episode, "City of Lost Children" (bonus points for moderately obscure French sci-fi reference): Mon-El is the former High Prince of Planet Daxam, which was basically Sparta to Krypton's Athens - a monarchist caste-based society with a frat-party social philosophy - and was destroyed by the space-debris from when its more-enlightened neighbor became its more-exploded neighbor. His life-pod having crashed on Earth (leading him to assume he was the sole survivor), Mon-El teamed up with Supergirl and the D.E.O. after becoming smitten with Kara and deciding he'd like to atone for having been a rich jerk his whole life by becoming a superhero. Helpfully, Daxamites have roughly similar superpowers to Kryptonians on Earth, and as a bonus the attraction is reciprocated... even though he neglected to mention his royal heritage until King Lar-Gand and Queen Rhea turned up alive and looking to take him back.
Plotwise, that all seems to be coming to a head in advance of the season finale at the end of the month: Mon-El has told his parents (who want him to help rebuild Daxam as a potentially even more classist party-planet) that he wants to stay on Earth with Kara, Queen Rhea has declared her intent to force him to change his mind (going so far as to kill her husband when he disagreed) and has manipulated Lena Luthor (short version: Mommy Issues) into helping her teleport a battle fleet into Earth's orbit for backup. But in the season-long buildup to this point, Mon-El's episode-to-episode character arc has been largely centered on one key facet of his (literal) super-training: Learning to embrace the value of self-sacrifice.
Specifically, these lessons have included: Putting the protection of others ahead of his desire to put down villains, prioritizing the greater-good over his reflexive desire to protect his mentor/girlfriend and (see above) willingly giving up his old life because his position required the subjugation of others. If you were a TV story-supervisor plotting out the thematic beats of the series without any names or mythos-specific details to work from, the ultimate resolution of a story-arc like that wouldn't even be a question. Of course, the story would end with Mon-El making the ultimate act of self-sacrifice by giving up his own life to stop (or help stop, since after all this isn't his show) his evil mother - thus bringing his arc to a close by exiting a season-long storyline he kicked off by arriving.
But will they go that route? Supergirl's writing staff has demonstrated a penchant for swerving on conventional story formula and expected beats in the past, most notably by essentially saying "gotcha!" on the buildup to Kara's budding romance with James Olsen from season 1 - sending her off to mentor/fall for Mon-El and having Olsen take up vigilantism as The Guardian (as origin stories go, "post-breakup inadequacy-anxiety" is at least original...) - but also in the way it kept fans guessing about Lena Luthor's loyalties and the offbeat repurposing of DC Comics fixtures like Cyborg Superman and Miss Martian. So perhaps Mon-El (himself repurposed from a moderately-obscure Superman Family side-character at one point also called "Valor") will end up in different role than what he seems thematically destined for.
One thing working against that prospect is the question of what purpose his character would serve, narratively, if he were to stick around after Queen Rhea's defeat - a conclusion that seems somewhat foregone given that teases for season 3 are already touting a new main villain. While Mon-El has an arc of his own, as a supporting character in an ensemble series his main overall function is to help drive the overarching story and themes of the series. In this case that's meant contributing to season 2's central focus on confronting prejudice, which has saddled most of the main characters with either an external or internal prejudice of their own to either overcome, confront or both as a reflection of the season-long storyline about Supergirl and The D.E.O. battling Lilian Luthor's anti-alien-immigration hate group CADMUS.
Alex Danvers has confronted the influence of homophobia after coming out as a lesbian, Martian Manhunter J'onn J'onzz has had to work through his hatred of White Martians upon meeting M'gann M'orzz ("Miss Martian"), Lena Luthor is driven by a desire to prove herself to a world that judges her by her infamous family name and President Marsdin (Lynda Carter) has sought out Supergirl as the public face of her push for amnesty for the same alien immigrants targeted by CADMUS. For her own part, Kara has had to get over her long-held biases against Daxamites - and her relationship (both pre and mid-romantic) with Mon-El has been the through-line for that development.
But said development has, well... developed. She's "over it," even after having met a living embodiment of her own preconceptions in Rhea and learning that Mon-El was lying about a fairly big part of his own story. With that having been accomplished, in terms of narrative mechanics that leaves Mon-El himself without a part to play - at least, not one that doesn't completely upend the series foundational scenario: Supergirl has been built and sold as a show with a central protagonist and supporting characters in her orbit - not a double-act. It is, effectively, "The Kara Show" and not "The Adventures of The Super-Couple"... and that's about the only direction it can go if Mon-El becomes Kara's permanent live-in equally-powered partner (and that's not even getting into what having "super backup" on call at all times does to the series' ability to build suspense).
There are other possibilities that don't necessarily involve the character dying or sticking around in the same capacity. Mon-El could head off on superheroic missions of his own (maybe to chase Bad Mom through space, should Rhea exit the series in retreat rather than final defeat. He could be injured or depowered in some way, which would minimize the issue of writing around his current role as Kara's stay-at-home trump-card. One way or another, though, unless Supergirl is prepared to go into season 3 as a substantially different show than what's made it a success in the first place; fans of the Super Couple pairing should probably get ready for a less than happy ending.