Normal portal link range of a portal to establish link to another one is not sufficient. After placing 4 (or less) link amplifiers and establish links and fields, if I remove the link amp(s) to replace them with some other modules will the links and fields be broken?
Long links and fields will remain even after the Link Amp mod is destroyed. However, as of August 28th, it is not possible to remove portal mods, unless the mod is destroyed by an attack! Hence - the Link Amp mods can't be removed and changed to a different (i.e Portal Shield) mod until attacked by the enemy.
No, links and fields will remain.
What you describe is a good strategy for making mega fields more resistant to attack :D. Once the field is done, replace link amp with very rare shields and your portal will be much more difficult to destroy (unless of use of virus :( )
EDIT (28/08/2013) : As described by @idan315, there was an update yesterday that limit mod placing. Only 1 mod per portal per player, and no more removal allowed...
The strategy explained before will no longer be possible.