To better illuminate the purpose of this post's title and content, I'd like to start by elaborating upon my usage of "apathy". It is, within our relevant context, a loss of interest in a specific facet of tabletop gaming (as opposed to disillusionment with the entire convention). Whether that be a specific role (Host/Player), game (WH40K/D&D), genre (Hyper-Realism/High Fantasy), or some combination of the three. The disinterest in these factors, while unique to any given situation, can range from a gradual erosion in general enjoyment, to a sudden, overwhelming abhorrence for all things relating to the offender in question. Such gross reactions, though seldom, can serve as the catalyst for the disbandment of an otherwise stable group; a fate I hope to help circumvent with the possible alternatives/remedies listed below.
Options for the Burned-Out Host
Hosting responsibilities tend to be rather inflexible; that is, once a group has designated one of their own as "The Host/GM/DM/etc.", they tend to retain the position for most of the foreseeable future. While this may be in the best interest for the Players and/or the group as a whole, a few months (or even years!) of this can leave even the best of us jaded and embittered.
Edit: Case in point (http://www.penny-arcade.com/comic/2010/12/13/)
So, before quitting in a huff, try these first:
Ideally, your group would be cycling between each others' places of residence, but even if your abode is the sole locale available for gaming, the duties of running the actual sessions can easily be rotated on a regular basis. To implement this plan, all one needs is a concise, written summary of the overarching plot and the key details/events pertaining thereof. With this blueprint as a guide, each Player can create their own minor details that make up the bulk of play time; instilling a mechanic not entirely unlike the traditional game in which individuals sit around and take turns adding improvisational chapters onto an original story one of them had initially started.
Has running the same genre/system/theme for a year or so drained you of your vitality? Perhaps some communication with the Players is in order. If they aren't receptive to the idea of switching games mid-campaign, offer the possibility of adding another day of gaming to your schedule, reserved specifically for a new, fresh style of play (barring the implementation of yet another day of gaming, perhaps a rotation of content within your existing schedule could be negotiated?).
-Skip a Session (or two)
Sometimes nothing beats stepping back and recollecting yourself (tactfully done, of course). The promise of new, freshly inspired content after the lapse in activity will certainly win over even the most staunch objectors.
Options for the Burned-Out Player
For the typical purveyor of tabletop war gaming, the prospect of forming and assembling an army is one of great commitment and dedication. Unfortunately, this investment of resources can be quite regretful, if one finds themselves suddenly dissatisfied with their forces. This may be inflicted by a seemingly drastic change in game play rules or a simple matter of stagnation. In any case, your options are admittedly limited, but a trusted friend with similar interests may be open to the idea of temporarily trading figurines; permitting you both a new experience and a deeper understanding of the game in question.
If you've been consistently stuck as the burly, hard-hitting tank of your gaming group, perhaps it's high time to try your hand the squishy, nimble ranged fighter. If the other Players simply can't do without their veteran damage sponge, an alteration of mere aesthetics or role playing style may do. Instead of the usual dashing, armor-clad paladin that absorbs punishment with a collection of iron and magic, the role of a drunken, uncouth man-mountain of prodigious muscular fortitude could be a refreshing change.
-Skip a Session (or two)
Much like the Host, a properly excused leave of absence can work wonders for one's creatives processes. Just make sure whomever is in charge of your character's actions in the meantime has both of your best interests in mind (or is an impartial party, in the very least).
It's my best hopes that you've found the above material to be informative, concise, and sufficient in preserving the integrity of your group's collective enjoyment. The loss of passion for something that once fascinated yourself and others is truly a terrible thing and I'm happy to do what I can to avert/correct such malady.