Heck, a road question! That's what I do in my day job...
You don't say what period your book is set in. So I'll try to cover all bases:
Early medieval, non-Roman, Tolkien - the roads are probably just dirt tracks. They will get rutted over time. When it rains they will get muddy, sometimes impassable. Crossing rivers might be a bit tricky. Unless someone has kindly built a bridge, you will probably have to cross at a ferry point or a ford. Or swim.
These sorts of road are okayish for one person, but not very good at transporting large numbers of people, heavy goods or delicate things (pottery, glass). So as we move into industrial times folks tend to invent metalled roads and/or canals and railways.
Roman - an invading army builds stone roads and bridges. The roads are mostly straight because it's the shortest distance between two points and as an invading army they don't care who owns the land they are building over.
Late Medieval - enterprising capitalists and/or far thinking communities invent turnpike roads. People using the roads are charged a toll which is used to pay for the repair of the road. There are often different levels of tolls for different types of road user - horse, mule, carriage, etc.
Modern era - roads are paid for through taxation. In some rare cases, road users are charged directly for the use of a road, tunnel or a bridge.
So in tough times would roads fall into disrepair?
In early medieval times, no. They are not maintained anyway, so you wouldn't notice a difference.
In Roman times, also probably no. The invading army would want to keep their lines of communication working.
In late medieval, possibly. Turnpike roads don't always work and they weren't universal. Some unscrupulous road operators would take the money from the tolls and not do the repair work.
In a modern setting, certainly. Road spending can fall if the Government doesn't raise enough in taxes or spends that money on something else.