I'll ignore the internal motivation question(s) and address [briefly]
What has been the government's response to the protestors so far?
Probably nothing, given that only 100 people showed up at that protest in Kyiv, according to LA Times. (Protest which only happened 2 days ago. The newspaper also says that "scores" of people showed up in 6 other cites.)
As for lack/sparsity of rotations from the front line, let alone letting soldiers end their service altogether after a set period, I found this from February.
We asked the General Staff what the rotation procedure is and whether all those who have been fighting for a long time will be replaced. We were told that they do not comment on these topics.
Anyhow, the Ukrainian media (citing some UK gov't source) says that Russian troops aren't getting much rotations either, so that's probably part of the implicit semi-official response.
Also, it looks like Zelenskyy himself addressed that demobilization [after set period] Q before:
Citizens have registered several electronic petitions on the president's website, asking [...] to allow the military, who have been at war for a year, to demobilize. However, a similar petition had already gained 25,000 votes, and both Defense Minister Reznikov and President Zelenskyy responded that in wartime, military personnel can be demobilized only in accordance with Article 26 of the Law of Ukraine “On Military Duty and Military Service” — upon reaching the age of 60, for health reasons, due to a court conviction, etc.
FWTW, for perspective, around 19,000 Ukrainians tried to flee across the borders to avoid the draft but were caught. (And surely some uncounted number succeeded.)
According to Le Monde,
Ukrainian soldiers are rarely granted leave due to a lack of replacements.
That piece says that rather than being demobilized (as those protesters asked) some soldiers were given a 10 day leave after 1.5 years. And that was instead of the 30 days allowed in peace time.
There's a bit more info on the troubles that Ukraine has with keeping the ranks filled, published more recently in Time
according to U.S. and European estimates, the toll has long surpassed 100,000 on each side of the war. It has eroded the ranks of Ukraine’s armed forces so badly that draft offices have been forced to call up ever older personnel, raising the average age of a soldier in Ukraine to around 43 years. “They’re grown men now, and they aren’t that healthy to begin with,” says the close aide to Zelensky. “This is Ukraine. Not Scandinavia.”
The picture looked different at the outset of the invasion. One branch of the military, known as the Territorial Defense Forces, reported accepting 100,000 new recruits in the first 10 days of all-out war. The mass mobilization was fueled in part by the optimistic predictions of some senior officials that the war would be won in months if not weeks. “Many people thought they could sign up for a quick tour and take part in a heroic victory,” says the second member of the President’s team.
Now recruitment is way down. As conscription efforts have intensified around the country, stories are spreading on social media of draft officers pulling men off trains and buses and sending them to the front. Those with means sometimes bribe their way out of service, often by paying for a medical exemption. Such episodes of corruption within the recruitment system became so widespread by the end of the summer that on Aug. 11 Zelensky fired the heads of the draft offices in every region of the country.
The decision was intended to signal his commitment to fighting graft. But the move backfired, according to the senior military officer, as recruitment nearly ground to a halt without leadership. The fired officials also proved difficult to replace, in part because the reputation of the draft offices had been tainted. “Who wants that job?” the officer asks. “It’s like putting a sign on your back that says: corrupt.”
This is no doubt related to the long service periods for those already drafted, probably in more than one way. E.g. some probably have qualms about volunteering now given the apparently indefinite period that they might need to serve. And vice-versa, the lack of sufficient new volunteers means that those already serving need to do long tours with little leave. It's a catch-22 in some ways.
FWTW, Russia also appears to be lengthening the tours of duty. At least those of prisoners. No more getting pardoned after 6 months. Now they have to serve till the end of the war.
WaPo reported on Feb 8 that the personnel situation was pretty dire for the Ukrainians:
Oleksandr, a battalion commander, said the companies in his unit on average are staffed at about 35 percent of what they should be. A second battalion commander from an assault brigade said that is typical for units that carry out combat tasks. [...]
Especially in winter, when the weather conditions are hard, infantry should be rotated out after about three days. But because units lack troops, deployments get extended — or personnel intended for the rear get pressed into front-line duty despite being ill-prepared for it.
Serhiy, 41, a platoon commander fighting in Avdiivka, the site of Russia’s most intense assaults, said he and his men are rarely rotated out after just three days. More often five days go by — or even 10.
Dmytro, another deputy battalion commander in a different brigade, said his infantry typically get two days of rest after five to 10 days holding the line, and because most of his soldiers are over the age of 40, their lack of physical fitness compounds the problems. [...]
The lack of rotations is a problem across the Ukrainian military — not just for infantry on the line. Soldiers might get a few days off to go home and see their families, but rarely more. They say they are still motivated to fight the Russian invaders, but also that they need rest and more men beside them.
