Usually cases of a slowly decreasing amount of water are that a filter has become clogged. Does your water supply have sand particles coming through? Check the diverter heads for other faucets in the house. Are they getting many small particles trapped in them? Sand in one faucet tells you that all fixtures are getting clogged, some more slowly than others. This sandy junk can come through municipal water systems, or it can come from your own well if you are on one.
If you are getting much of this coming through, you may choose to install a whole house water filter to prevent that.
Whatever you find in those other faucets, if the problem is both the shower head and the tub spout, then the problem is in the fixture itself. Is this one of the new style fixtures that regulates the temperature of the water? I have read that those temperature regulators can sometimes be a problem themselves, improperly shutting down water flow.
If not that, assuming this is a cartridge based fixture, then you will need to pull the cartridge from the faucet. This entails removing the handle, then removing a locking nut that holds it together. Please shut off the water BEFORE you do any of this! The cartridge will come out, although this sometimes takes some amount of persuasion.
You can buy either a complete cartridge replacement from most manufacturers, or just a set of new o-rings etc., to rebuild the cartridge. Large home centers will have an entire wall filled with various such replacements. Bring in the old cartridge if possible to get a match. Knowing what company made your fixture will help.
A possibility is that a piece of rubber from an o-ring or other seal has cracked and become lodged in an orifice inside the cartridge. Look for this, or for other problems when you open up the cartridge.
Best Answer
For copper pipe, hot (~50 C) water should only flow at approx 5 ft/second. Flow of less than one or two ft/sec can also be a problem. Based on the diameter of the pipe (1/2 in type L), 0.72 gpm flows at 1.0 ft/second, so this would suggest a maximum of 3.6 gpm for the pipe (assuming 5 ft/second). Also, you must worry about the pressure drop. Use table 6 of The copper Handbook, at 5 gpm, the pressure loss is 0.161 psi/ft. Assuming your supply is 50 psi, and you need 35 psi to be delivered to the shower head, you can have a maximum pipe length of (50-35)/.161=93 ft. Figure 7 shows how fittings should be counted due to their larger pressure drop. A 90 degree fitting counts as one foot. Additionally, water pressure will decrease with elevation by approximately 0.433 psi/foot.
As long as you meet these two restrictions, you're fine. Since you need 4.5 gpm, and your pipe is likely less than 93 feet, things should work fine.