I don't know why, but sometimes if that happens to me (typically going from wi-fi to cell and needing it to hop onto the cell network), merely going into airplane mode and then turning airplane mode off fixes that problem. That's kinda the reverse situation, but you might give that a try. Make SURE your wi-fi icon is by default "on."
Lately, I've also noticed that sometimes my phone doesn't promptly hook onto my home wi-fi network and sometimes stays on the cell network when I (a) turn on the router in my home and (b) bring the phone out of airplane mode (which I typically use when I sleep). In those instance, I don't have toggle airplane mode again. Just touching the wi-fi icon and make sure to toggle it on does the trick.
Reboots work but are never required in these circumstances. So, try toggling airplane mode, or even just wi-fi on and off. That seems to jiggle it into making the connection.