In this example, "fragile" is a bit odd because it is being said directly to the person. The common meanings are physically fragile (as in the case of an old person who has fallen and broken some bones) and emotionally fragile (as in the case of a child-like person who gets overly sad or overly angry about everyday events). Benjamin Pike's understanding as "emotionally sensitive" is probably the only interpretation.

When describing a person, "fragile" typically means that they are very sensitive emotionally. Maybe they cry or become otherwise upset easily. It really depends on context, but quite often this is a negative characteristic, meaning that the person is overly sensitive and cannot control their emotions. The example you give doesn't quite make sense to me. I don't think it's appropriate to describe Ann as fragile in the context of offering praise. It comes off as a bit patronizing, in my opinion.

I interpret this as being 'sensitive' - easy to upset or thin skinned. Can't say for sure without knowing much more about the character.

It means delicate, someone cannot handle big upheavals. 小家碧玉