"Taper" means to diminish or reduce in size or impact, to dwindle. To provide further help, "admonish" means yell at, scold; "shirk" means avoid a responsibility; "thrive" and "flourish" are synonyms, both words means to grow and develop very well. 

To "affect" something means to have an impact on, to influence, to change. One of the more challenging differentiations in definitions that English speakers have to deal with can be found in "affect" and "effect." To "affect" means to influence; the "effect" is the result, the consequence. So, you "affect" something to produce an "effect." To provide further help, "onset" means beginning; "demonstrate" means show, provide an example; "startle" means to shock or surprise. 

To "fumble" means to drop something, to do something careless and clumsy with one's hands. 

To "wrench" means to pull suddenly or violently, to tug, to yank. To provide further help, "loathe" means hate; "jest" means joke; "leap" means jump high. 

To "uproot" means to force someone from their home, or place they are comfortable in, and make them move elsewhere. To provide further help, "dismember" means take apart; "encroach" means trespass, intrude on another person's property; "succumb" means give in to, fail to resist; "demise" means death.

"Transpire" means to take place, to happen, to occur. To provide further help, "misplace" means lose; "eradicate" means get rid of, completely eliminate; "frighten" means scare; "acknowledge" means recognize, notice. 

"Materialize" means to happen, to transpire, to occur, to take place, to become real and take place. To provide further help, "partition" means divide; "cleave" means split in two, divide; "toss" means throw; "lend" means allow someone to borrow. 

To "cringe" means to recoil, to turn away from or back away from in fear or disgust or embarrassment. To provide further help, "migrate" means move from one place to another; "extradite" means deport, allow someone to be taken out of a country so that they can be tried for crimes committed in another country; "banish" means send someone away as punishment and not allow them to return; deplore" means hate, loathe. 

To "persevere" means to keep going in the fact of difficulty. As such it is closest in meaning to "continue." To provide further help, "postulate" means suggest a possible theory, estimate; "halt" means stop, pause; "hesitate" means to pause or delay before saying or doing something; "aggregate," when used as a verb, means to combine, to come together. 

Perhaps you have heard of soil erosion. This is the process of topsoil wearing away from various causes. Often, water is involved in this process, though not necessarily always. That does not really matter for this question, in any case. The general idea is that erosion pertains to the "breaking down" of something over a period of time. The only option that expresses this idea is "dissolve." This is a very distant synonym—but a synonym nonetheless.