Because despite winning the Punic wars, it apsolutely gave the Republic a beating. Apparently 1/5 of the male population of Rome died in the war.
Money
People
Infrastructure
How long did it take for each to grow back?
Of the things you mention I can only give a reliable answer for manpower. Infrastructure is way too complicated (What would you count? How would you could the infrastructure of defected allies? What sources would you use?). Money might be a bit easier, but economic history is not my cup of tea. Given the large indemnity paid by Carthage and the huge amounts of loot the Romans carried from Greece in the 190s BC, I'd say they'd have recovered money-wise within a decade.
Manpower then. Here is part of a table from De Ligt, using census figures mostly from Livy (and a couple of other sources):
| Year (BC) | Census figure |
|---|---|
| 241/0 | 260,000 |
| 234/3 | 270,313 |
| 209/8 | 137,108 |
| 204/3 | 214,000 |
| 194/3 | 243,704* |
| 189/8 | 258,318 |
| 179/8 | 258,794 |
| 174/3 | 269,015 |
| 169/8 | 312,805 |
(*De Ligt lists "143,704" in his table, citing Livy 35.9. Livy lists 243,704. I have corrected this error here.)
As you can see before the Second Punic War there were 270 thousand adult male Roman citizens. By 209, after several disastrous years, this had dropped to 137 thousand. After that recovery was pretty quick, a couple of decades to get back to almost the number of citizens in 234 BC. But it would take until the year 169 before the previous high was broken. So that's four decades before there was full recovery in manpower.
Let's have a look at the average number of Roman legions in the field during this period of recovery (numbers taken from Rich):
| Period | avg # of legions |
|---|---|
| 200-196 | 8 |
| 195-191 | 9 |
| 190-186 | 11 (Seleucid War) |
| 185-181 | 8 |
| 180-176 | 8 |
| 175-171 | 8 |
| 170-166 | 8 |
As you can see, from 185 onwards the demands on manpower were pretty stable, while the available manpower was growing. This means that from the huge peak during the Second Punic War (as much as 50% of citizens serving at some times) and the slightly less large spike during the Seleucid War (about 25%), the percentage of available manpower serving in legions gradually dropped to 10% in the middle of the 2nd century. That's a lot healthier a percentage than the percentages during the major wars mentioned earlier.
Sources: