Such is life
Basically, the ideal where everyone makes it to every session to have a steadily continuing epic adventure is poorly compatible with many realities of a typical adult life. People have obligations towards their employers, their friends and their families, and those obligations are often serious enough to override the importance of playing this night.
Damage control
Absences are something you can't get rid of, but you can work towards having your game being more allowing of them. The core idea is that the game exists for the players, not vice versa - if the game and the players interact poorly, it's much easier and considerate to change the game to fit the players than to try to change the players. There are some tricks to reduce the impact of absences:
- don't focus any session on a particular PC without a backup plan
- agree conventions on how absent players' PCs are handled (for example, our absent players' PCs are just "somewhere on the background")
- if you want all PCs to be available each session, have the players agree on substitutes so each PC has a backup player and determine their boundaries (eg. control in combat situations versus control everywhere)
- avoid puzzles and challenges relying on remembering things from previous sessions
- keep the plot simple and/or keep a shared adventure log somewhere
If possible, you can also try changing your campaign's style from a continuous one towards a more episodic direction. The more self-contained each session is, the less bothersome absences are. For example, in one of my games, every session's adventure begun and ended in the relative safety of the same village. Absent players' characters were simply doing something else that was agreed between the GM and their players, eg. our Ranger's player was absent so the Ranger spent the session training the village's bowmen. The Ranger's day spent training the archers was briefly narrated at the beginning of the next session.
Every session being roughly self-contained worked very well to keep the game working smoothly despite very regularly missing at least one player. However, it can be hard to pull off in some systems; eg. in DnD 5e it is hard to fit a single dungeon in a single session consistently, while in Dungeon World it's easier to have a few days' worth of semi-intense adventuring in as much time.
Words of warning
You may be tempted to try "tiering" your sessions by player presence: "important" sessions where everyone's present and the plot advances, and "filler" sessions for keeping the present players entertained for one session when you don't want to advance the plot too much in the others' absence. While it's not a bad idea in itself, be aware that frequent absences can all but stall the progress of the adventure, which may frustrate your players and yourself. I know because this happened to me: an important session was postponed by several months of filler sessions because we couldn't find a time when everyone could make it. Therefore I advise exercising caution when tiering sessions, and try adapting to player absences in other ways instead.
It's a fairly common thing in the RPG scene to punish players for absences in various ways. The most typical one is withholding experience and other goodies from PCs whose players didn't participate, which has little impact in some systems but can make characters unenjoyably weak compared to their peers in others. I strongly urge you to avoid this and any other kind of punishment for absences, especially since having to skip sessions on a short notice is understandable for parents or those with a lot of responsibilities in their jobs. Punishing absences assumes bad faith where there is none, and serves no purpose in making the game feel welcoming to the frequent absentee(s).
Rebrand "frequent absentee" as "Guest Star"
Finally, if a player is absent very often, you can work their sporadic presence in as a part of your game (with the player's consent, of course). You can give them a special role of narrative significance, something between a PC and NPC, such as a celestial being, wise old sage or mysterious samurai who pops up intermittently to assist the other PCs in their adventures and leaves afterwards. (This is also a cool way, when premeditated with the player, to have a character death for drama without having to sacrifice any of the "real" PCs -- in one of our games, a player had agreed for his character to die in secrecy with the GM, and it came as a huge yet cool shock for us players.)
In mechanically complex systems like many editions of DnD, this makes life easier for the "guest star" as they don't have to spend time and effort keeping track of their character between sessions and can instead use simplified mechanics (eg. those of a suitable monster in DnD). You can also offer any "guest stars" the opportunity to be a Harlequin - a player who plays some or all of the NPCs the players encounter.
Bottom line
Accommodating your game for a person with frequent absences may seem tricky, and you may have to give away things you wanted to have in your games to pull it off in a satisfying manner. However, it also signals your frequently absent players that their presence in your table is welcomed and enjoyed, and that is worth a lot.
