Which is grammatically correct and why?
- Members are requested to pay their subscriptions in time.
- All the Members are requested to pay their subscriptions in time.
The first is a request, the second a description of procedure.
Both are grammatically correct, but they are used in different contexts.
Members are requested to ....
is a very formal, polite way to give an order. You often hear it on aircraft, e.g.:
Passengers are requested to return to their seats, fasten their seatbelts, and return their seats to the upright position.
This is probably the form that you should be using.
All the members are requested to ...
is not usually used to give instructions. You are just describing the situation. E.g.:
All the members are requested to pay their subscriptions on time, but more than 20% pay late.
This isn't a grammar problem but a semantics question:
Is there a difference between saying "Members are" and "All members are"?
I think the default assumption is that they are equivalent, unless it's common and accepted practice in the club for some members to pay their dues late.
I also think the phrase in time should be changed to on time. The former phrase means to do something before something else happens, e.g.,
Be at the station in time to find a seat on the train or you'll have to stand.
The latter means to do something before the deadline, i.e., in a timely manner, e.g.,
Please pay your dues on time. If you're late too often, you will be asked to pay a 10% surcharge.
Using members, the sentence addresses the group of people comprising members as a unit.
Using all members, on the other hand, addresses individual members.
The difference, as Bill Franke has noted, is not one of grammar but semantics. It may be important, say, from a protocol point of view.