Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
BusyCal Brings iCloud Calendars To Snow Leopard
There are many Mac users who have upgraded to the Mac OS X Lion, but are still operating on the technology of Mac OS X Snow Leopard. The reasons for this act are quite obvious. The applications are performing much better on the Snow Leopard than they are on the Mac OS X Lion. The main point of problem in Mac OS X Lion is that all the work is done with the help of the different applications and not by the operating system itself.
Among many, a major reason to lag behind Lion was the up gradation of the MobileMe account to the iCloud application as no one wants to lose access onto the shared MobileMe calendars that are made part of the application. Although, this was not the only machine mix, as access to those calendars are also required that are originally on the system and the same cannot be upgraded to the Snow Leopard version and the Power Mac G5 file server which has seemed to get stuck up at version Leopard 10.5. The same problem persists with the iPhones and iPads but, since Apple has devised the iOS 5 technology for them, the cloud computing service poses no serious problems for them.
The upgrading to the iCloud service from the account of MobileMe, simply means that the user will no longer be able to use the shared calendar option as is offered in MobileMe which might turn out to be in serious conflicts between the schedules that are shared via the calendar option among associates.
It is for sure that there may be several Mac users who have not yet upgraded to the iCloud because of this issue and capturing the market affected with this problem, a software developing company BusyMac, has released software under the name of BusyCal which has eventually resolved the issue. This feature has been especially designed to enable all Mac users operating on Mac OS X 10.5 Leopard and later versions to share the calendars of iCloud. But, this does not mean that you switch to iCloud on this single reason as there is one significant barrier which is still persisting with the BusyCal 1.6.1 and it is that before the finishing of the process takes place, it was thought that all the older Macs will be integrated within the mix by issuing all the shared iCloud calendars by making use of an local network of BusyCal to BusyCal sharing which turned out to be simply unnecessary.
Moreover, there are several other causalities which are associated in the process of switching to iCloud of which only one problem can be considered as a significant one. Several types of data which includes Dock items, Dashboard widgets, Preferences, and Mail accounts, signatures, Keychains, rules, as well as smart mailboxes cannot be synchronized once you have upgraded to the iCloud application. This is also applicable on independent applications which greatly rely on Mac operating systems synchronization services to sync data from across all Macs such as Yojimbo, Transmit, TextExpander, and several other such applications. But, if you are using the DropBox application, this issue can also be resolved to a greater extent as it serves as a viable option for syncing within the MobileMe and it is also expected that the up gradations within the application of MobileMe will include the factor of support of synchronization within the iCloud. Another matter of concern is that the Address Book syncing is lost on a Mac which is not operating on Lion, as there are not many people which are in desperate need for Contact syncing with non-Lion Mac operating systems, still the feature of Address Book Server provides several features which enables both contact as well as calendar syncing onto a local network and the best thing is that currently the service is offered free of cost.
Concluding the overall situation, it can be said that moving to iCloud application do have an associated problem of losing the calendar sharing option which is the base for people using iCal, but the fact which is preferred is that the application of BusyCal imposes by all means that the transition from MobileMe to iCloud services is far easier than it has been anticipated.