Were you on the synthroid for Hashimoto's autoimmune thyroiditis?
If so, then yes, your thyroid function can change over time.
Hashimoto's thyroidiits is a chronic, life-long condition where your white blood cells produce antibodies (special proteins) that attack your thyroid gland.
Roughly 5% of patients with Hashimoto's thyroiditis lose their thyroid function per year, so most patients actually have some thyroid function even though their gland is under autoimmune attack.
But thyroid levels can fluctuate over time. It is sort of a balance between how badly your immune system is attacking your gland, how well your gland can still produce thyroid hormone (i.e. how much of the working gland is still left after the immune destruction), and how much your brain responds to the destruction by the feedback loop:
When your thyroid level drops, say from autoimmune destruction, your brain senses this and releases TSH or thyroid stimulating hormone. TSH in turn acts on your thyroid to tell it to crank up it's thyroid hormone production.
Many people with untreated Hashimoto's disease will have high levels of TSH, since their brains are trying to tell their thyroid to crank up the production of thyroid hormone.
Typically, the endocrinologist will check your TSH level and use this to help decide/monitor how much thyroid hormone to give you. Many endocrinologists keep the TSH at the lower end of normal- about 0.5... This can help keep you energized, and it can help prevent a goiter from forming (where your thyroid gland gets too big because it is trying too hard to make hormone)
If your TSH drops too low on the thyroid replacement, they may back of for a while, since it is very dangerous to have too much thyroid hormone (it can cause a lot of problems).

As if this weren't complicated enough, sometimes with Hashimoto's thyroiditis, your gland can just dump out large amounts of thyroid hormone, and you may get temporarily too much thyroid hormone in your blood. This may drop your TSH temporarily too. It's called "Hashitoxicosis".

And then even more complicated are the rare cases where you can actually have not just the antibodies of hashimoto's disease, but those of Grave's disease as well, which bind to the TSH receptors and stimulate (or sometimes inhibit) them...

It's a complicated illness with so many reasons for the thyroid hormone levels to fluctuate.
Great fun, as thyroid hormone controls the metabolism and functioning of virtually every cell in the body!

You have my deepest sympathy!