##TL;DR: Because they have no idea where to look.
It would take at least 50 years to search all of Georgia for her, and along the way, they'd encounter ten million zombies and die.
##What they know:
Daryl is the only person who was there when Beth disappeared, and here's the sum total of useful information he shared:
Daryl: I was with Beth. We got out together. I was with her for a while.
Rick: Is she dead?
Daryl: She's just gone.
- The Walking Dead, S4E16, A
So Maggie knows nothing beyond "Beth is gone". That isn't much to work with.
##Places to look:
The United States is a huge country - about 4,000,000 mi2. The contiguous United States is about 3,000,000 mi2. It is roughly 3,000 miles from east to west, and 1,500 miles north to south. People have walked across the country in less than 2 months, but on average, it takes 6-8 months at a reasonable pace.
There are almost 20,000 villages, towns and cities in the country, and 134,000,000 homes. Let's say it takes an average of 5 minutes to search a home - not counting travel time, it would take about 11,200,000 hours (465,000 days; 1,300 years) to search every home in the country.
Even if we assume that she's somewhere in Georgia, that leaves us with 60,000 mi2, 535 towns and cities, containing a total of 3,600,000 homes to search, which would still take us 35 years of searching.
Add to that 680,000 registered businesses in Georgia, and 30,000,000 nationwide. There are nearly 6,000,000 commercial buildings in the US - about 1/5 the number of businesses. If we assume that this ratio is true of Georgia, that leaves us with 136,000 commercial buildings to search. If it takes 5 minutes to search a commercial building, that will add another year and a half to the search time.
Let's assume it takes them two minutes to move from one building to the next (it would take seconds to get from one building to the next within a town, but it might take hours to walk from one town to the next, so we'll average it out to two minutes). Grand total: 50 years of looking for Beth.
##What they'll be dealing with while they search:
There are 10,215,000 people in Georgia. The ratio of zombies to humans in The Walking Dead is 5,000 to 1. That means they'll probably run into 10,213,000 zombies along the way.
There were 16 people in the group after they reunited. In seasons 1-4, the group killed 956 zombies, and eight of them were killed by zombies. This means that one person died for every 120 zombies killed. At that rate, they will only be able to kill 1,920 zombies - about 0.019% of the total - before they're all dead.
#Conclusion:
###They have no information about where she might be, and if they decided to look for her, it would take them at least 50 years to search every building in the state. While they're looking, they'll run into over ten million zombies, and they'll all be dead before they've searched a meaningful percentage of the state. Maggie loves Beth, but not enough to get 16 people killed on a 50-year-long search of the entire state of Georgia.