Manual of the Planes implies that the portal's immobile
The prestige class planeshifter gains at level 10 the natural ability demiplane seed (Manual of the Planes (Sept. 2001) 31–2). Over the course of the demiplane seed ability's 300-word description, only this sentence mentions the portal that connects the planeshifter's demiplane to elsewhere: The planeshifter's demiplane "has a single portal entry, which the planeshifter may control for access" (32). The class just doesn't offer any more details.
By default, this means that the portal to the planeshifter's demiplane is the same as any other Manual of the Planes-style portal (that are slightly different from, for example, Forgotten Realms-style and Stronghold Builder's Guide-style portals). Manual of the Planes on Magic Portals says that the word portal "is a general term for a stationary interplanar connection. Portals… open at one location on the originating plane and at one location on the destination plane (or planes)" (21 and emphasis mine).
This means that when the planeshifter finishes the 100-day process that's required to create her personal demiplane, the planeshifter's player talks to the DM about where the portal that leads to her demiplane is, and that's where that portal stays. Forever. And, to be clear, the planeshifter can't use again her demiplane seed ability until all portals that lead to that demiplane are destroyed. And, moreover, so far as I can tell, Manual of the Planes contains no information on how to destroy its portals. For example, from the same book, even the 6th-level Sor/Wiz spell seal portal [abjur] (MP 39), only prevents a portal from being used instead of destroying it (or instead of creating a portal that's only accessible by pinnipeds like it should).
Were information included about destroying these kinds of portals in Manual or even in the Planar Handbook that was published after the 3.5 revision, it'd be a thing for a planeshifter to employ the demiplane seed ability, cast divinations to learn the demiplane's tuning fork material and frequency (see here), destroy the portal that leads to the planeshifter's demiplane, then make another demiplane. Through such a convoluted process the planeshifter could accumulate—ever so slowly (we're talkin' years)—a series of extradimensional safe houses that only the planeshifter could conveniently access. Except that there just aren't any rules for destroying these kinds of portals. So. Um. Yeah.
What that means and what you may want to do about it
I'm pretty sure that readers familiar with the evolution of Dungeons & Dragons, Third Edition will agree that the demiplane seed ability is—in almost every way—totally horrible, inferior to almost every other way of creating one's own demiplane (e.g. here). Further, the prestige class planeshifter is itself not a particularly well-balanced class as a creature that takes it is typically at least level 9 (because of the entry requirement that she be able to cast 5th-level spells) who then gives up 3 levels of spellcasting advancement (therefore typically delaying her 9th-level spells until character level 20) for class features that are—for the most part—just toys, and, really, the ability demiplane seed is, here, just a toy, and it's not even a very fun one like her 100-ft.-radius telepathy and her at-will spell-like ability plane shift.
However, readers should keep in mind that Manual of the Planes was published only shortly after the much-maligned Psionics Handbook and its 9th-level power genesis [metacreativity] (77 with the link to the updated version of the power from the Expanded Psionics Handbook)—it bearing a passing resemblance to the ability demiplane seed—that was at the time the only means available for most creatures to create their own demiplanes (excluding, of course, extradimensional containers and the like; see here).
Manual was also published only shortly after the Forgotten Realms Campaign Setting (June 2001) and—maybe because work was conducted on both books simultaneously?— Manual doesn't include Forgotten's coverage of the oops?-they're-slightly-different Forgotten-style portals. In addition, Manual dates to well before both Deities and Demigods (Apr. 2002) and the Epic Level Handbook (July 2002) that both include the much more useful, palatable, and–above all—convenient 9th-level spell genesis [conj] (DD 216 and EL 117, respectively, with the linked description having been drawn from the latter) that just allows a caster—still with some effort, of course—to toss off a spell that makes a demiplane, no prestige class capstone ability or psionics required.
With all this in mind, the Dungeon Master's Guide on Why a Revision? says that the 3.5 revision "is compatible with existing products [like Manual of the Planes], and these products can be used with the revision with only minor adjustments" (4), and one of the minor adjustments the DM should make is to the prestige class planeshifter and especially to its demiplane seed ability.
What exactly those adjustments should be will depend mightily on the campaign, but I suspect lowering the entry requirements alone wouldn't be enough. For example, in this DM's campaigns, access to a relatively secret and generally habitable demiplane remains an ability suitable only for mid- to high-level PCs (e.g. about level 10 or later), so were one of this DM's players to express an interest in the prestige class planeshifter, this DM might just lower the ability demiplane seed to level 1, allow multiple demiplanes at level 3, allow the creation of new portals to her demiplanes at level 5, and so on to make that feature the class's centerpiece. As is, if the demiplane seed ability is why the player's looking at the prestige class planeshifter, she's better off at level 9 or higher just buying an attuned gem of genesis (33,100 gp; 0 lbs.) (Magic of Faerûn 14, 21), crushing it on the Ethereal Plane, then continuing doing what she's doing.