This question appears to have gone unanswered, but the answer is "No, you are not stuck with it". You can put your domestic spies to supporting your party in power, which will reduce the support of all other parties, eventually reducing them to the point that no party but the one in power has high enough support to demand a cabinet position. When that happens the fractured government modifier will go away and stay gone. Be warned, though, it takes a long time sometimes and is best done from the beginning of the game.
Edit: but of course CK is also right that you need to evaluate whether it is worth bothering to this much trouble to remove a penalty when it might be having negligible net effect on your nation.
In fact, I use this little game fact as an offense tool on certain occasions. If I want a particular country to surrender more quickly due to low NU, then rather than have my spies go right at the NU mission, I first have them spend a goodly while raising the support of MY party in that country. That will almost always result in fractured government because nations in differing factions also tend to have parties in power which are ideologically aligned with that faction, meaning any party whose ideology aligns with a different faction is not going to be well represented in the pool of potential ministers. Example, USA has very few Bund ministers, so if Germany raises the Bund's support the USA will not have enough potential ministers to fill the number of posts required to avoid the penalty. Then once that penalty is likely well underway, I switch to counterespionage for a little while to clear out the domestic spies in that country (don't want them supporting their own party back up) and then I switch to lowering NU. At this point there are now two penalties being applied at the same time, the fractured govt and the direct effect of my spies. Of course attacking another country's NU only really works if you have the time to go at it long term before you even face them in battle.1